Finite Group Databasebeta

← Group #13140205

Character table — Group #13140205

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order122222223666666644121212123366666666666666366666661212121212121212121212121212121244444444444422444466661212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ911-1-111-1-11111-1-1-1-1i−iii−i−i111111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i11-1-1ii−i−i1-11-1i−i11-1-1ii−i−iii−i−i11-1-111-1-1ii−i−i
χ1011-1-111-1-11111-1-1-1-1i−iii−i−i111111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i-1-111−i−iii-111-1−ii-1-111−i−iiiii−i−i11-1-1-1-111−i−iii
χ1111-1-111-1-11111-1-1-1-1i−iii−i−i111111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii11-1-1−i−iii-11-11i−i-1-111−i−iii−i−iii-1-11111-1-1ii−i−i
χ1211-1-111-1-11111-1-1-1-1i−iii−i−i111111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii-1-111ii−i−i1-1-11−ii11-1-1ii−i−i−i−iii-1-111-1-111−i−iii
χ1311-1-111-1-11111-1-1-1-1−ii−i−iii111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−i11-1-1ii−i−i-11-11−ii-1-111ii−i−iii−i−i-1-11111-1-1−i−iii
χ1411-1-111-1-11111-1-1-1-1−ii−i−iii111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-111−i−iii1-1-11i−i11-1-1−i−iiiii−i−i-1-111-1-111ii−i−i
χ1511-1-111-1-11111-1-1-1-1−ii−i−iii111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii11-1-1−i−iii1-11-1−ii11-1-1−i−iii−i−iii11-1-111-1-1−i−iii
χ1611-1-111-1-11111-1-1-1-1−ii−i−iii111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii-1-111ii−i−i-111-1i−i-1-111ii−i−i−i−iii11-1-1-1-111ii−i−i
χ1722222222222222222222222-122-1-122-1-12-12-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-10000222200000000220000000000000000-1-1-1-1-1-1-1-1
χ1822222222222222222222222-122-1-122-1-12-12-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-200000000-2-2000000000000000011111111
χ192222222222222222222222-12-1-122-1-122-12-12-12-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122220000000000220000000000-1-1-1-1-1-1-1-100000000
χ202222222222222222222222-12-1-122-1-122-12-12-12-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-2-2-2-20000000000-2-200000000001111111100000000
χ212222222222222222-2-2-2-2-2-22-122-1-122-1-12-12-12-1-1-1-1-1-1-1-1-1-2-211-2-211111111110000222200000000-2-20000000000000000-1-1-1-11111
χ222222222222222222-2-2-2-2-2-22-122-1-122-1-12-12-12-1-1-1-1-1-1-1-1-1-2-211-2-211111111110000-2-2-2-2000000002200000000000000001111-1-1-1-1
χ232222222222222222-2-2-2-2-2-2-12-1-122-1-122-12-12-12-1-1-1-1-1-1-1-111-2-211-2-21111111122220000000000-2-20000000000-1-1-1-1111100000000
χ242222222222222222-2-2-2-2-2-2-12-1-122-1-122-12-12-12-1-1-1-1-1-1-1-111-2-211-2-211111111-2-2-2-200000000002200000000001111-1-1-1-100000000
χ25222-2-2-2-2222-2-22-2-22000000222-22-2222-2-2-2-2-2-2222-2-222-2-2000000000000000000002i−2i2i−2i000000000000000000000000002i−2i2i−2i0000
χ26222-2-2-2-2222-2-22-2-22000000222-22-2222-2-2-2-2-2-2222-2-222-2-200000000000000000000−2i2i−2i2i00000000000000000000000000−2i2i−2i2i0000
χ27222-2-2-2-2222-2-22-2-220000002-12-2-1122-11-21-21-2-1-1-111-1-111003−3003−333−3−333−3−300002i−2i2i−2i00000000000000000000000000−ii−ii−i3i3−i3i3
χ28222-2-2-2-2222-2-22-2-220000002-12-2-1122-11-21-21-2-1-1-111-1-111003−3003−333−3−333−3−30000−2i2i−2i2i00000000000000000000000000i−ii−ii3−i3i3−i3
χ29222-2-2-2-2222-2-22-2-220000002-12-2-1122-11-21-21-2-1-1-111-1-11100−3300−33−3−333−3−33300002i−2i2i−2i00000000000000000000000000−ii−iii3−i3i3−i3
χ30222-2-2-2-2222-2-22-2-220000002-12-2-1122-11-21-21-2-1-1-111-1-11100−3300−33−3−333−3−3330000−2i2i−2i2i00000000000000000000000000i−ii−i−i3i3−i3i3
χ3122-22-2-22-222-2-2-222-2000000222-22-2-2-2-2222-2-22-222-2-2-2-222000000000000000000002i−2i−2i2i000000000000000000000000002i−2i−2i2i0000
χ3222-22-2-22-222-2-2-222-2000000222-22-2-2-2-2222-2-22-222-2-2-2-22200000000000000000000−2i2i2i−2i00000000000000000000000000−2i2i2i−2i0000
χ3322-22-2-22-222-2-2-222-20000002-12-2-11-2-21-12-1-2121-1-11111-1-100−i3i300i3−i3−i3−i3i3i3i3i3−i3−i300002i−2i−2i2i00000000000000000000000000−iii−i−333−3
χ3422-22-2-22-222-2-2-222-20000002-12-2-11-2-21-12-1-2121-1-11111-1-100−i3i300i3−i3−i3−i3i3i3i3i3−i3−i30000−2i2i2i−2i00000000000000000000000000i−i−ii3−3−33
χ3522-22-2-22-222-2-2-222-20000002-12-2-11-2-21-12-1-2121-1-11111-1-100i3−i300−i3i3i3i3−i3−i3−i3−i3i3i300002i−2i−2i2i00000000000000000000000000−iii−i3−3−33
χ3622-22-2-22-222-2-2-222-20000002-12-2-11-2-21-12-1-2121-1-11111-1-100i3−i300−i3i3i3i3−i3−i3−i3−i3i3i30000−2i2i2i−2i00000000000000000000000000i−i−ii−333−3
χ3722-2-222-2-22222-2-2-2-22i−2i2i2i−2i−2i2-122-1-1-2-211-212-1-21-1-1-1-111112i2i−i−i−2i−2iii−i−i−i−iiiii000022-2-2000000002i−2i0000000000000000-1-111−i−iii
χ3822-2-222-2-22222-2-2-2-22i−2i2i2i−2i−2i2-122-1-1-2-211-212-1-21-1-1-1-111112i2i−i−i−2i−2iii−i−i−i−iiiii0000-2-22200000000−2i2i000000000000000011-1-1ii−i−i
χ3922-2-222-2-22222-2-2-2-22i−2i2i2i−2i−2i-12-1-12211-2-21-2-121-2-1-1-1-11111−i−i2i2iii−2i−2i−i−i−i−iiiii2i2i−2i−2i00000000002-20000000000−i−iii-1-11100000000
χ4022-2-222-2-22222-2-2-2-22i−2i2i2i−2i−2i-12-1-12211-2-21-2-121-2-1-1-1-11111−i−i2i2iii−2i−2i−i−i−i−iiiii−2i−2i2i2i0000000000-220000000000ii−i−i11-1-100000000
χ4122-2-222-2-22222-2-2-2-2−2i2i−2i−2i2i2i2-122-1-1-2-211-212-1-21-1-1-1-11111−2i−2iii2i2i−i−iiiii−i−i−i−i000022-2-200000000−2i2i0000000000000000-1-111ii−i−i
χ4222-2-222-2-22222-2-2-2-2−2i2i−2i−2i2i2i2-122-1-1-2-211-212-1-21-1-1-1-11111−2i−2iii2i2i−i−iiiii−i−i−i−i0000-2-222000000002i−2i000000000000000011-1-1−i−iii
χ4322-2-222-2-22222-2-2-2-2−2i2i−2i−2i2i2i-12-1-12211-2-21-2-121-2-1-1-1-11111ii−2i−2i−i−i2i2iiiii−i−i−i−i2i2i−2i−2i0000000000-220000000000−i−iii11-1-100000000
χ4422-2-222-2-22222-2-2-2-2−2i2i−2i−2i2i2i-12-1-12211-2-21-2-121-2-1-1-1-11111ii−2i−2i−i−i2i2iiiii−i−i−i−i−2i−2i2i2i00000000002-20000000000ii−i−i-1-11100000000
χ452-2222-2-2-22-22-22-22-200000022-22-2-22-22-222-22-2-22-22-22-2-2200000000000000002i−2i2i−2i00000000000000000000002i−2i2i−2i000000000000
χ462-2222-2-2-22-22-22-22-200000022-22-2-22-22-222-22-2-22-22-22-2-220000000000000000−2i2i−2i2i0000000000000000000000−2i2i−2i2i000000000000
χ472-2222-2-2-22-22-22-22-2000000-121-1-2-2-112-2-12121-2-11-11-111-1−i3i300−i3i300−i3i3−i3i3−i3i3−i3i32i−2i2i−2i0000000000000000000000−ii−ii3−33−300000000
χ482-2222-2-2-22-22-22-22-2000000-121-1-2-2-112-2-12121-2-11-11-111-1−i3i300−i3i300−i3i3−i3i3−i3i3−i3i3−2i2i−2i2i0000000000000000000000i−ii−i−33−3300000000
χ492-2222-2-2-22-22-22-22-2000000-121-1-2-2-112-2-12121-2-11-11-111-1i3−i300i3−i300i3−i3i3−i3i3−i3i3−i32i−2i2i−2i0000000000000000000000−ii−ii−33−3300000000
χ502-2222-2-2-22-22-22-22-2000000-121-1-2-2-112-2-12121-2-11-11-111-1i3−i300i3−i300i3−i3i3−i3i3−i3i3−i3−2i2i−2i2i0000000000000000000000i−ii−i3−33−300000000
χ512-22-2-222-22-2-2222-2-200000022-2-2-222-222-2-22-22-22-2-222-22-20000000000000000000000002i−2i2i−2i00000000002i−2i2i−2i0000000000000000
χ522-22-2-222-22-2-2222-2-200000022-2-2-222-222-2-22-22-22-2-222-22-2000000000000000000000000−2i2i−2i2i0000000000−2i2i−2i2i0000000000000000
χ532-2-22-22-222-2-22-2-22200000022-2-2-22-22-2-2222-2-222-2-22-22-220000000000000000000000002-2-2200000000002-2-220000000000000000
χ542-2-22-22-222-2-22-2-22200000022-2-2-22-22-2-2222-2-222-2-22-22-22000000000000000000000000-222-20000000000-222-20000000000000000
χ552-2-2-22-2222-22-2-22-2200000022-22-2-2-22-22-2-2-22222-22-2-222-200000000000000002-2-2200000000000000000000002-2-22000000000000
χ562-2-2-22-2222-22-2-22-2200000022-22-2-2-22-22-2-2-22222-22-2-222-20000000000000000-222-20000000000000000000000-222-2000000000000
χ572-2-2-22-2222-22-2-22-22000000-121-1-2-21-1-221-212-12-11-111-1-113−300−33003−33−3−33−332-2-220000000000000000000000-111-1−333−300000000
χ582-2-2-22-2222-22-2-22-22000000-121-1-2-21-1-221-212-12-11-111-1-113−300−33003−33−3−33−33-222-200000000000000000000001-1-113−3−3300000000
χ592-2-2-22-2222-22-2-22-22000000-121-1-2-21-1-221-212-12-11-111-1-11−33003−300−33−333−33−32-2-220000000000000000000000-111-13−3−3300000000
χ602-2-2-22-2222-22-2-22-22000000-121-1-2-21-1-221-212-12-11-111-1-11−33003−300−33−333−33−3-222-200000000000000000000001-1-11−333−300000000
χ614444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-211111111-2-2-2-2-2-2-2-211111111000000000000000000000000000000000000000000
χ624444444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111122222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000
χ63444-4-4-4-4444-4-44-4-44000000-24-224-4-2-24-42-42-424-2-222-2-2220000000000000000000000000000000000000000000000000000000000
χ64444-4-4-4-4444-4-44-4-44000000-2-2-22-22-2-2-2222222-211-1-111-1-10023−230023−23−3−333−3−333000000000000000000000000000000000000000000
χ65444-4-4-4-4444-4-44-4-44000000-2-2-22-22-2-2-2222222-211-1-111-1-100−232300−232333−3−333−3−3000000000000000000000000000000000000000000
χ6644-44-4-44-444-4-4-444-4000000-24-224-422-44-242-4-2-4-2-22222-2-20000000000000000000000000000000000000000000000000000000000
χ6744-44-4-44-444-4-4-444-4000000-2-2-22-22222-2-2-222-2211-1-1-1-11100−2i32i3002i3−2i3i3i3−i3−i3−i3−i3i3i3000000000000000000000000000000000000000000
χ6844-44-4-44-444-4-4-444-4000000-2-2-22-22222-2-2-222-2211-1-1-1-111002i3−2i300−2i32i3−i3−i3i3i3i3i3−i3−i3000000000000000000000000000000000000000000
χ6944-4-444-4-44444-4-4-4-44i−4i4i4i−4i−4i-2-2-2-2-2-2222222-2-2221111-1-1-1-1−2i−2i−2i−2i2i2i2i2iiiii−i−i−i−i000000000000000000000000000000000000000000
χ7044-4-444-4-44444-4-4-4-4−4i4i−4i−4i4i4i-2-2-2-2-2-2222222-2-2221111-1-1-1-12i2i2i2i−2i−2i−2i−2i−i−i−i−iiiii000000000000000000000000000000000000000000
χ714-4444-4-4-44-44-44-44-40000004-2-44224-4-224-2-4-2-42-22-22-222-20000000000000000000000000000000000000000000000000000000000
χ724-4444-4-4-44-44-44-44-4000000-2-22-222-22-22-2-22-2221-11-11-1-11−2i32i300−2i32i300i3−i3i3−i3i3−i3i3−i3000000000000000000000000000000000000000000
χ734-4444-4-4-44-44-44-44-4000000-2-22-222-22-22-2-22-2221-11-11-1-112i3−2i3002i3−2i300−i3i3−i3i3−i3i3−i3i3000000000000000000000000000000000000000000
χ744-44-4-444-44-4-4444-4-40000004-2-4-42-24-4-2-2-424242-222-2-22-220000000000000000000000000000000000000000000000000000000000
χ754-44-4-444-44-4-4444-4-4000000-2422-44-22442-4-2-4-2-4-222-2-22-220000000000000000000000000000000000000000000000000000000000
χ764-44-4-444-44-4-4444-4-4000000-2-2222-2-22-2-222-22-221-1-111-11-1000000003i−3i−3i3i3i−3i−3i3i000000000000000000000000000000000000000000
χ774-44-4-444-44-4-4444-4-4000000-2-2222-2-22-2-222-22-221-1-111-11-100000000−3i3i3i−3i−3i3i3i−3i000000000000000000000000000000000000000000
χ784-4-44-44-444-4-44-4-4440000004-2-4-42-2-44224-242-4-2-222-22-22-20000000000000000000000000000000000000000000000000000000000
χ794-4-44-44-444-4-44-4-444000000-2422-442-2-4-4-24-2-424-222-22-22-20000000000000000000000000000000000000000000000000000000000
χ804-4-44-44-444-4-44-4-444000000-2-2222-22-222-2-2-222-21-1-11-11-11000000003-3-33-333-3000000000000000000000000000000000000000000
χ814-4-44-44-444-4-44-4-444000000-2-2222-22-222-2-2-222-21-1-11-11-1100000000-333-33-3-33000000000000000000000000000000000000000000
χ824-4-4-44-4444-44-4-44-440000004-2-4422-442-2-42-4-24-2-22-222-2-220000000000000000000000000000000000000000000000000000000000
χ834-4-4-44-4444-44-4-44-44000000-2-22-2222-22-2222-2-2-21-11-1-111-123−2300−232300−33−333−33−3000000000000000000000000000000000000000000
χ844-4-4-44-4444-44-4-44-44000000-2-22-2222-22-2222-2-2-21-11-1-111-1−23230023−23003−33−3−33−33000000000000000000000000000000000000000000
χ8566666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000000000002222220000-1-1-1-1-1-1-1-10000000000000000
χ8666666666-3-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000000000000000-2-2-2-2-2-20000111111110000000000000000
χ8766666666-3-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000000000000000002222-2-200001111-1-1-1-10000000000000000
χ8866666666-3-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000000000000000-2-2-2-2220000-1-1-1-111110000000000000000
χ8966-6-666-6-6-3-3-3-333336i−6i−3i−3i3i3i0000000000000000000000000000000000000000000000002i2i−2i−2i2-20000-1-111−i−iii0000000000000000
χ9066-6-666-6-6-3-3-3-333336i−6i−3i−3i3i3i000000000000000000000000000000000000000000000000−2i−2i2i2i-22000011-1-1ii−i−i0000000000000000
χ9166-6-666-6-6-3-3-3-33333−6i6i3i3i−3i−3i0000000000000000000000000000000000000000000000002i2i−2i−2i-22000011-1-1−i−iii0000000000000000
χ9266-6-666-6-6-3-3-3-33333−6i6i3i3i−3i−3i000000000000000000000000000000000000000000000000−2i−2i2i2i2-20000-1-111ii−i−i0000000000000000
χ936-66-6-666-6-333-3-3-3330033−3333−330000000000000000000000000000000000000000000000002i−2i2i−2i000000−i3i3−i3i3−ii−ii0000000000000000
χ946-66-6-666-6-333-3-3-3330033−3333−33000000000000000000000000000000000000000000000000−2i2i−2i2i000000i3−i3i3−i3i−ii−i0000000000000000
χ956-66-6-666-6-333-3-3-33300−3333−33330000000000000000000000000000000000000000000000002i−2i2i−2i000000i3−i3i3−i3−ii−ii0000000000000000
χ966-66-6-666-6-333-3-3-33300−3333−3333000000000000000000000000000000000000000000000000−2i2i−2i2i000000−i3i3−i3i3i−ii−i0000000000000000
χ976-6-66-66-66-333-333-3-300−3i33i33i3−3i30000000000000000000000000000000000000000000000002-2-22000000−i3i3i3−i3-111-10000000000000000
χ986-6-66-66-66-333-333-3-300−3i33i33i3−3i3000000000000000000000000000000000000000000000000-222-2000000i3−i3−i3i31-1-110000000000000000
χ996-6-66-66-66-333-333-3-3003i3−3i3−3i33i30000000000000000000000000000000000000000000000002-2-22000000i3−i3−i3i3-111-10000000000000000
χ1006-6-66-66-66-333-333-3-3003i3−3i3−3i33i3000000000000000000000000000000000000000000000000-222-2000000−i3i3i3−i31-1-110000000000000000
χ101121212-12-12-12-1212-6-666-666-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1021212-1212-12-1212-12-6-6666-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-12121212-12-12-12-66-66-66-660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-12-12-1212-121212-66-666-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).