Finite Group Databasebeta

← Group #13140134

Character table — Group #13140134

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order1222222236666666441212121233666666666666663666666612121212121212121212121212121212444444444444444444121212121212121212121212121212121212121212121212
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
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911-1-11-11-1111-1-1-11-1i−iii−i−i111111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-11-11-1i−iii−i−i11-1-1ii−i−i11-1-111-1-1ii−i−i
χ1011-1-11-11-1111-1-1-11-1i−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−i−iii-1-111-111-1−ii−i−iii-1-111ii−i−i11-1-1-1-111−i−iii
χ1111-1-11-11-1111-1-1-11-1i−iii−i−i111111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iiiii−i−i-1-1111-1-11−iiii−i−i11-1-1−i−iii-1-111-1-111−i−iii
χ1211-1-11-11-1111-1-1-11-1i−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−i−iii11-1-1-11-11i−i−i−iii-1-111−i−iii-1-11111-1-1ii−i−i
χ1311-1-11-11-1111-1-1-11-1−ii−i−iii111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i11-1-1-11-11−iiii−i−i-1-111ii−i−i-1-11111-1-1−i−iii
χ1411-1-11-11-1111-1-1-11-1−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−i−iii-1-1111-1-11i−i−i−iii11-1-1ii−i−i-1-111-1-111ii−i−i
χ1511-1-11-11-1111-1-1-11-1−ii−i−iii111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iiiii−i−i-1-111-111-1i−iii−i−i-1-111−i−iii11-1-1-1-111ii−i−i
χ1611-1-11-11-1111-1-1-11-1−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−i−iii11-1-11-11-1−ii−i−iii11-1-1−i−iii11-1-111-1-1−i−iii
χ1722222222222222222222222-122-1-122-1-12-12-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-10000000022220000220000000000000000-1-1-1-1-1-1-1-1
χ1822222222222222222222222-122-1-122-1-12-12-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-100000000-2-2-2-20000-2-2000000000000000011111111
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
χ212222222222222222-2-2-2-2-2-22-122-1-122-1-12-12-12-1-1-1-1-1-1-1-1-1-2-211-2-211111111110000000022220000-2-20000000000000000-1-1-1-11111
χ222222222222222222-2-2-2-2-2-22-122-1-122-1-12-12-12-1-1-1-1-1-1-1-1-1-2-211-2-2111111111100000000-2-2-2-200002200000000000000001111-1-1-1-1
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
χ25222-2-22-2-222-222-2-2-2000000222-22-22-222-2-2-2-22-222-2-222-2-200000000000000002-22-200000000000000000000002-22-2000000000000
χ26222-2-22-2-222-222-2-2-2000000222-22-22-222-2-2-2-22-222-2-222-2-20000000000000000-22-220000000000000000000000-22-22000000000000
χ27222-2-22-2-222-222-2-2-2000000-12-112-2-11221-21-2-1-2-1-111-1-1113−3003−30033−3−333−3−32-22-20000000000000000000000-11-113−33−300000000
χ28222-2-22-2-222-222-2-2-2000000-12-112-2-11221-21-2-1-2-1-111-1-1113−3003−30033−3−333−3−3-22-2200000000000000000000001-11-1−33−3300000000
χ29222-2-22-2-222-222-2-2-2000000-12-112-2-11221-21-2-1-2-1-111-1-111−3300−3300−3−333−3−3332-22-20000000000000000000000-11-11−33−3300000000
χ30222-2-22-2-222-222-2-2-2000000-12-112-2-11221-21-2-1-2-1-111-1-111−3300−3300−3−333−3−333-22-2200000000000000000000001-11-13−33−300000000
χ3122-22-2-2-2222-2-2-22-22000000222-22-2-22-2-222-2-2-2222-2-2-2-22200000000000000002i−2i−2i2i00000000000000000000002i−2i−2i2i000000000000
χ3222-22-2-2-2222-2-2-22-22000000222-22-2-22-2-222-2-2-2222-2-2-2-2220000000000000000−2i2i2i−2i0000000000000000000000−2i2i2i−2i000000000000
χ3322-22-2-2-2222-2-2-22-22000000-12-112-21-1-2-2-121-212-1-11111-1-1−i3i300i3−i300−i3−i3i3i3i3i3−i3−i32i−2i−2i2i0000000000000000000000−iii−i−333−300000000
χ3422-22-2-2-2222-2-2-22-22000000-12-112-21-1-2-2-121-212-1-11111-1-1−i3i300i3−i300−i3−i3i3i3i3i3−i3−i3−2i2i2i−2i0000000000000000000000i−i−ii3−3−3300000000
χ3522-22-2-2-2222-2-2-22-22000000-12-112-21-1-2-2-121-212-1-11111-1-1i3−i300−i3i300i3i3−i3−i3−i3−i3i3i32i−2i−2i2i0000000000000000000000−iii−i3−3−3300000000
χ3622-22-2-2-2222-2-2-22-22000000-12-112-21-1-2-2-121-212-1-11111-1-1i3−i300−i3i300i3i3−i3−i3−i3−i3i3i3−2i2i2i−2i0000000000000000000000i−i−ii−333−300000000
χ3722-2-22-22-2222-2-2-22-22i−2i2i2i−2i−2i2-122-1-1-2-211-212-1-21-1-1-1-111112i2i−i−i−2i−2iii−i−i−i−iiiii0000000022-2-200002i−2i0000000000000000-1-111−i−iii
χ3822-2-22-22-2222-2-2-22-22i−2i2i2i−2i−2i2-122-1-1-2-211-212-1-21-1-1-1-111112i2i−i−i−2i−2iii−i−i−i−iiiii00000000-2-2220000−2i2i000000000000000011-1-1ii−i−i
χ3922-2-22-22-2222-2-2-22-22i−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
χ4022-2-22-22-2222-2-2-22-22i−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
χ4122-2-22-22-2222-2-2-22-2−2i2i−2i−2i2i2i2-122-1-1-2-211-212-1-21-1-1-1-11111−2i−2iii2i2i−i−iiiii−i−i−i−i0000000022-2-20000−2i2i0000000000000000-1-111ii−i−i
χ4222-2-22-22-2222-2-2-22-2−2i2i−2i−2i2i2i2-122-1-1-2-211-212-1-21-1-1-1-11111−2i−2iii2i2i−i−iiiii−i−i−i−i00000000-2-22200002i−2i000000000000000011-1-1−i−iii
χ4322-2-22-22-2222-2-2-22-2−2i2i−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
χ4422-2-22-22-2222-2-2-22-2−2i2i−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
χ452-222-2-22-22-222-22-2-200000022-2-2-2-22-22-22222-2-22-22-22-2-22000000000000000000002i−2i2i−2i00000000002i−2i2i−2i00000000000000000000
χ462-222-2-22-22-222-22-2-200000022-2-2-2-22-22-22222-2-22-22-22-2-2200000000000000000000−2i2i−2i2i0000000000−2i2i−2i2i00000000000000000000
χ472-22-22-2-222-2-22-2-22200000022-22-22222-2-2-2-2-2-222-2-222-22-20000000000000000000000002i−2i2i−2i00000000000000000000002i−2i2i−2i0000
χ482-22-22-2-222-2-22-2-22200000022-22-22222-2-2-2-2-2-222-2-222-22-2000000000000000000000000−2i2i−2i2i0000000000000000000000−2i2i−2i2i0000
χ492-22-22-2-222-2-22-2-2220000002-1-221-122-11-21-21-2-1-111-1-11-11003−3003−33−33−33−33−3000000002i−2i2i−2i0000000000000000000000−ii−ii−i3i3−i3i3
χ502-22-22-2-222-2-22-2-2220000002-1-221-122-11-21-21-2-1-111-1-11-11003−3003−33−33−33−33−300000000−2i2i−2i2i0000000000000000000000i−ii−ii3−i3i3−i3
χ512-22-22-2-222-2-22-2-2220000002-1-221-122-11-21-21-2-1-111-1-11-1100−3300−33−33−33−33−33000000002i−2i2i−2i0000000000000000000000−ii−iii3−i3i3−i3
χ522-22-22-2-222-2-22-2-2220000002-1-221-122-11-21-21-2-1-111-1-11-1100−3300−33−33−33−33−3300000000−2i2i−2i2i0000000000000000000000i−ii−i−i3i3−i3i3
χ532-2-2222-2-22-2-2-2222-200000022-22-22-2-2-2222-2-22-22-2-22-22-220000000000000000000000002i−2i−2i2i00000000000000000000002i−2i−2i2i0000
χ542-2-2222-2-22-2-2-2222-200000022-22-22-2-2-2222-2-22-22-2-22-22-22000000000000000000000000−2i2i2i−2i0000000000000000000000−2i2i2i−2i0000
χ552-2-2222-2-22-2-2-2222-20000002-1-221-1-2-21-12-1-2121-111-11-11-100−i3i300i3−i3−i3i3−i3i3i3−i3i3−i3000000002i−2i−2i2i0000000000000000000000−iii−i−333−3
χ562-2-2222-2-22-2-2-2222-20000002-1-221-1-2-21-12-1-2121-111-11-11-100−i3i300i3−i3−i3i3−i3i3i3−i3i3−i300000000−2i2i2i−2i0000000000000000000000i−i−ii3−3−33
χ572-2-2222-2-22-2-2-2222-20000002-1-221-1-2-21-12-1-2121-111-11-11-100i3−i300−i3i3i3−i3i3−i3−i3i3−i3i3000000002i−2i−2i2i0000000000000000000000−iii−i3−3−33
χ582-2-2222-2-22-2-2-2222-20000002-1-221-1-2-21-12-1-2121-111-11-11-100i3−i300−i3i3i3−i3i3−i3−i3i3−i3i300000000−2i2i2i−2i0000000000000000000000i−i−ii−333−3
χ592-2-2-2-22222-22-22-2-2200000022-2-2-2-2-22-22-2-222222-22-2-222-2000000000000000000002-2-2200000000002-2-2200000000000000000000
χ602-2-2-2-22222-22-22-2-2200000022-2-2-2-2-22-22-2-222222-22-2-222-200000000000000000000-222-20000000000-222-200000000000000000000
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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
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χ976-6-6-6-6666-33-33-333-30033−33−3333000000000000000000000000000000000000000000002-2-220000000000-111-1−333−30000000000000000
χ986-6-6-6-6666-33-33-333-30033−33−333300000000000000000000000000000000000000000000-222-200000000001-1-113−3−330000000000000000
χ996-6-6-6-6666-33-33-333-300−333333−33000000000000000000000000000000000000000000002-2-220000000000-111-13−3−330000000000000000
χ1006-6-6-6-6666-33-33-333-300−333333−3300000000000000000000000000000000000000000000-222-200000000001-1-11−333−30000000000000000
χ101121212-12-1212-12-12-6-66-6-66660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1021212-1212-12-12-1212-6-6666-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-1212-1212-12-1212-666-666-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-12-12121212-12-12-6666-6-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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