Finite Group Databasebeta

← Group #13140112

Character table — Group #13140112

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order1222222236666666441212121233666666666666663666666612121212121212121212121212121212444444444444444444121212121212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
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
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
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
χ911-1-11-11-1111-1-11-1-11-111-1-111111-1-1-1-1-1-1-1111-1111-1-1-1-1111-1-111-1-11111-1-1-1-111-1-1ii−i−iii−i−i1-1i−ii−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i
χ1011-1-11-11-1111-1-11-1-11-111-1-111111-1-1-1-1-1-1-1111-1111-1-1-1-1111-1-111-1-11111-1-1-1-111-1-1−i−iii−i−iii1-1−ii−ii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii
χ1111-1-11-11-1111-1-11-1-11-111-1-111111-1-1-1-1-1-1-1111-1111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-111ii−i−i−i−iii-11i−i−iiii−i−iii−i−i-1-111-1-111−i−iii−i−iii
χ1211-1-11-11-1111-1-11-1-11-111-1-111111-1-1-1-1-1-1-1111-1111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-111−i−iiiii−i−i-11−iii−i−i−iii−i−iii-1-111-1-111ii−i−iii−i−i
χ1311-1-11-11-1111-1-11-1-1-11-1-11111111-1-1-1-1-1-1-1111-1111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-1ii−i−iii−i−i-11−ii−iiii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii
χ1411-1-11-11-1111-1-11-1-1-11-1-11111111-1-1-1-1-1-1-1111-1111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-1−i−iii−i−iii-11i−ii−i−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i
χ1511-1-11-11-1111-1-11-1-1-11-1-11111111-1-1-1-1-1-1-1111-1111-1-1-1-11-1-111-1-111-1-1-1-11111-1-111ii−i−i−i−iii1-1−iii−iii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i
χ1611-1-11-11-1111-1-11-1-1-11-1-11111111-1-1-1-1-1-1-1111-1111-1-1-1-11-1-111-1-111-1-1-1-11111-1-111−i−iiiii−i−i1-1i−i−ii−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222222-122-1222-1-1-1-12-1-12-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122220000000022000000000000-1-1-1-1-1-1-1-100000000
χ1822222222222222222222222-122-1222-1-1-1-12-1-12-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-2-20000000000001111111100000000
χ192222222222222222222222-12-1-12-1-1-12222-122-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000022220000220000000000000000-1-1-1-1-1-1-1-1
χ202222222222222222222222-12-1-12-1-1-12222-122-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000-2-2-2-20000-2-2000000000000000011111111
χ212222222222222222-2-2-2-2-2-22-122-1222-1-1-1-12-1-12-1-1-1-1-1-1-1-1-2-2-2-2111111111111222200000000-2-2000000000000-1-1-1-1111100000000
χ222222222222222222-2-2-2-2-2-22-122-1222-1-1-1-12-1-12-1-1-1-1-1-1-1-1-2-2-2-2111111111111-2-2-2-200000000220000000000001111-1-1-1-100000000
χ232222222222222222-2-2-2-2-2-2-12-1-12-1-1-12222-122-1-1-1-1-1-1-1-1-11111-2-2-2-2111111110000000022220000-2-20000000000000000-1-1-1-11111
χ242222222222222222-2-2-2-2-2-2-12-1-12-1-1-12222-122-1-1-1-1-1-1-1-1-11111-2-2-2-21111111100000000-2-2-2-200002200000000000000001111-1-1-1-1
χ25222-2-22-2-222-22-2-22-2000000222-2222-222-2-2-2-2-2-222-222-2-2-2000000000000000000002-22-200000000002-22-200000000000000000000
χ26222-2-22-2-222-22-2-22-2000000222-2222-222-2-2-2-2-2-222-222-2-2-200000000000000000000-22-220000000000-22-2200000000000000000000
χ2722-22-2-2-2222-2-22-2-22000000222-22-2-22-2-222-2-2-2222-2-2-222-2000000000000000000002i−2i−2i2i00000000002i−2i−2i2i00000000000000000000
χ2822-22-2-2-2222-2-22-2-22000000222-22-2-22-2-222-2-2-2222-2-2-222-200000000000000000000−2i2i2i−2i0000000000−2i2i2i−2i00000000000000000000
χ2922-2-22-22-2222-2-22-2-22-222-2-22-122-1-2-2-211112-1-1-2-1-1-11111-122-2-2-1-111-1-1-1-1111122-2-2000000002-2000000000000-1-111-1-11100000000
χ3022-2-22-22-2222-2-22-2-22-222-2-22-122-1-2-2-211112-1-1-2-1-1-11111-122-2-2-1-111-1-1-1-11111-2-22200000000-2200000000000011-1-111-1-100000000
χ3122-2-22-22-2222-2-22-2-22-222-2-2-12-1-12111-2-2-2-2-1221-1-1-11111-1-1-11122-2-2-1-1-1-11111000000002i2i−2i−2i00002i−2i0000000000000000−i−iii−i−iii
χ3222-2-22-22-2222-2-22-2-22-222-2-2-12-1-12111-2-2-2-2-1221-1-1-11111-1-1-11122-2-2-1-1-1-1111100000000−2i−2i2i2i0000−2i2i0000000000000000ii−i−iii−i−i
χ3322-2-22-22-2222-2-22-2-2-22-2-2222-122-1-2-2-211112-1-1-2-1-1-11111-1-2-22211-1-11111-1-1-1-122-2-200000000-22000000000000-1-11111-1-100000000
χ3422-2-22-22-2222-2-22-2-2-22-2-2222-122-1-2-2-211112-1-1-2-1-1-11111-1-2-22211-1-11111-1-1-1-1-2-222000000002-200000000000011-1-1-1-11100000000
χ3522-2-22-22-2222-2-22-2-2-22-2-222-12-1-12111-2-2-2-2-1221-1-1-11111-111-1-1-2-2221111-1-1-1-1000000002i2i−2i−2i0000−2i2i0000000000000000−i−iiiii−i−i
χ3622-2-22-22-2222-2-22-2-2-22-2-222-12-1-12111-2-2-2-2-1221-1-1-11111-111-1-1-2-2221111-1-1-1-100000000−2i−2i2i2i00002i−2i0000000000000000ii−i−i−i−iii
χ372-2222-2-2-22-2222-2-2-200000022-22-22-222-22-2-22-2-22-222-22-2-200000000000000002-22-200000000000000000000002-22-2000000000000
χ382-2222-2-2-22-2222-2-2-200000022-22-22-222-22-2-22-2-22-222-22-2-20000000000000000-22-220000000000000000000000-22-22000000000000
χ392-2222-2-2-22-2222-2-2-20000002-1-2212-22-11-11-2-11-2-11-1-11-11100003−33−333−3−333−3−32-22-20000000000000000000000-11-113−33−300000000
χ402-2222-2-2-22-2222-2-2-20000002-1-2212-22-11-11-2-11-2-11-1-11-11100003−33−333−3−333−3−3-22-2200000000000000000000001-11-1−33−3300000000
χ412-2222-2-2-22-2222-2-2-20000002-1-2212-22-11-11-2-11-2-11-1-11-1110000−33−33−3−333−3−3332-22-20000000000000000000000-11-11−33−3300000000
χ422-2222-2-2-22-2222-2-2-20000002-1-2212-22-11-11-2-11-2-11-1-11-1110000−33−33−3−333−3−333-22-2200000000000000000000001-11-13−33−300000000
χ432-22-2-2-2222-2-22-22-2200000022-2-2-22-2-22-2-222-2222-2-22-2-2220000000000000000000000002-22-200000000000000000000002-22-20000
χ442-22-2-2-2222-2-22-22-2200000022-2-2-22-2-22-2-222-2222-2-22-2-222000000000000000000000000-22-220000000000000000000000-22-220000
χ452-22-2-2-2222-2-22-22-22000000-1211-2-1112-2-22-1-22-1-111-111-1-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i3000000002-22-20000000000000000000000-11-11−i3i3−i3i3
χ462-22-2-2-2222-2-22-22-22000000-1211-2-1112-2-22-1-22-1-111-111-1-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i300000000-22-2200000000000000000000001-11-1i3−i3i3−i3
χ472-22-2-2-2222-2-22-22-22000000-1211-2-1112-2-22-1-22-1-111-111-1-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i3000000002-22-20000000000000000000000-11-11i3−i3i3−i3
χ482-22-2-2-2222-2-22-22-22000000-1211-2-1112-2-22-1-22-1-111-111-1-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i300000000-22-2200000000000000000000001-11-1−i3i3−i3i3
χ492-2-22-222-22-2-2-2222-200000022-2-2-2-222-222-22-22-22-2-2-222-220000000000000000000000002i−2i−2i2i00000000000000000000002i−2i−2i2i0000
χ502-2-22-222-22-2-2-2222-200000022-2-2-2-222-222-22-22-22-2-2-222-22000000000000000000000000−2i2i2i−2i0000000000000000000000−2i2i2i−2i0000
χ512-2-22-222-22-2-2-2222-2000000-1211-21-1-1-222-2-1-221-1111-1-11-1−i3i3i3−i30000−i3i3−i3i3i3−i3i3−i3000000002i−2i−2i2i0000000000000000000000−iii−i3−3−33
χ522-2-22-222-22-2-2-2222-2000000-1211-21-1-1-222-2-1-221-1111-1-11-1−i3i3i3−i30000−i3i3−i3i3i3−i3i3−i300000000−2i2i2i−2i0000000000000000000000i−i−ii−333−3
χ532-2-22-222-22-2-2-2222-2000000-1211-21-1-1-222-2-1-221-1111-1-11-1i3−i3−i3i30000i3−i3i3−i3−i3i3−i3i3000000002i−2i−2i2i0000000000000000000000−iii−i−333−3
χ542-2-22-222-22-2-2-2222-2000000-1211-21-1-1-222-2-1-221-1111-1-11-1i3−i3−i3i30000i3−i3i3−i3−i3i3−i3i300000000−2i2i2i−2i0000000000000000000000i−i−ii3−3−33
χ552-2-2-222-222-22-2-2-22200000022-22-2-22-2-22-22-22-222-22-22-22-200000000000000002-2-2200000000000000000000002-2-22000000000000
χ562-2-2-222-222-22-2-2-22200000022-22-2-22-2-22-22-22-222-22-22-22-20000000000000000-222-20000000000000000000000-222-2000000000000
χ572-2-2-222-222-22-2-2-2220000002-1-221-22-21-11-1-2-112-11-11-11-1100003−3−3333−3−3−3−3332-2-220000000000000000000000-111-13−3−3300000000
χ582-2-2-222-222-22-2-2-2220000002-1-221-22-21-11-1-2-112-11-11-11-1100003−3−3333−3−3−3−333-222-200000000000000000000001-1-11−333−300000000
χ592-2-2-222-222-22-2-2-2220000002-1-221-22-21-11-1-2-112-11-11-11-110000−333−3−3−33333−3−32-2-220000000000000000000000-111-1−333−300000000
χ602-2-2-222-222-22-2-2-2220000002-1-221-22-21-11-1-2-112-11-11-11-110000−333−3−3−33333−3−3-222-200000000000000000000001-1-113−3−3300000000
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
χ63444-4-44-4-444-44-4-44-40000004-24-4-244-4-2-222-422-4-2-22-2-22220000000000000000000000000000000000000000000000000000000000
χ64444-4-44-4-444-44-4-44-4000000-24-224-2-2244-4-42-4-42-2-22-2-22220000000000000000000000000000000000000000000000000000000000
χ65444-4-44-4-444-44-4-44-4000000-2-2-22-2-2-22-2-222222211-111-1-1-1000000003i−3i−3i3i3i−3i−3i3i000000000000000000000000000000000000000000
χ66444-4-44-4-444-44-4-44-4000000-2-2-22-2-2-22-2-222222211-111-1-1-100000000−3i3i3i−3i−3i3i3i−3i000000000000000000000000000000000000000000
χ6744-44-4-4-4444-4-44-4-440000004-24-4-2-4-4422-2-2-4224-2-2222-2-220000000000000000000000000000000000000000000000000000000000
χ6844-44-4-4-4444-4-44-4-44000000-24-22422-2-4-4442-4-4-2-2-2222-2-220000000000000000000000000000000000000000000000000000000000
χ6944-44-4-4-4444-4-44-4-44000000-2-2-22-222-222-2-2222-211-1-1-111-1000000003i−3i−3i3i−3i3i3i−3i000000000000000000000000000000000000000000
χ7044-44-4-4-4444-4-44-4-44000000-2-2-22-222-222-2-2222-211-1-1-111-100000000−3i3i3i−3i3i−3i−3i3i000000000000000000000000000000000000000000
χ7144-4-44-44-4444-4-44-4-44-444-4-4-2-2-2-2-22222222-2-2-22111-1-1-1-11-2-222-2-2221111-1-1-1-1000000000000000000000000000000000000000000
χ7244-4-44-44-4444-4-44-4-4-44-4-444-2-2-2-2-22222222-2-2-22111-1-1-1-1122-2-222-2-2-1-1-1-11111000000000000000000000000000000000000000000
χ734-4444-4-4-44-4444-4-4-4000000-242-2-4-22-24-44-424-42-22-2-22-2220000000000000000000000000000000000000000000000000000000000
χ744-4444-4-4-44-4444-4-4-4000000-2-22-22-22-2-22-222-2221-111-11-1-1000023−2323−23−3−333−3−333000000000000000000000000000000000000000000
χ754-4444-4-4-44-4444-4-4-4000000-2-22-22-22-2-22-222-2221-111-11-1-10000−2323−232333−3−333−3−3000000000000000000000000000000000000000000
χ764-44-4-4-4444-4-44-44-440000004-2-4-424-4-4-222-242-24-222-222-2-20000000000000000000000000000000000000000000000000000000000
χ774-44-4-4-4444-4-44-44-44000000-2-2222-222-222-2-22-2-21-1-11-1-111−2i32i3−2i32i30000i3−i3i3−i3i3−i3i3−i3000000000000000000000000000000000000000000
χ784-44-4-4-4444-4-44-44-44000000-2-2222-222-222-2-22-2-21-1-11-1-1112i3−2i32i3−2i30000−i3i3−i3i3−i3i3−i3i3000000000000000000000000000000000000000000
χ794-4-44-444-44-4-4-4444-40000004-2-4-42-4442-2-2242-2-4-2222-2-22-20000000000000000000000000000000000000000000000000000000000
χ804-4-44-444-44-4-4-4444-4000000-2-22222-2-22-2-22-22-221-1-1-111-11−2i32i32i3−2i30000i3−i3i3−i3−i3i3−i3i3000000000000000000000000000000000000000000
χ814-4-44-444-44-4-4-4444-4000000-2-22222-2-22-2-22-22-221-1-1-111-112i3−2i3−2i32i30000−i3i3−i3i3i3−i3i3−i3000000000000000000000000000000000000000000
χ824-4-4-444-444-44-4-4-444000000-242-2-42-22-44-4424-4-2-22-22-22-220000000000000000000000000000000000000000000000000000000000
χ834-4-4-444-444-44-4-4-444000000-2-22-222-222-22-22-22-21-11-11-11-1000023−23−2323−3−33333−3−3000000000000000000000000000000000000000000
χ844-4-4-444-444-44-4-4-444000000-2-22-222-222-22-22-22-21-11-11-11-10000−232323−2333−3−3−3−333000000000000000000000000000000000000000000
χ8566666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000000022220000002200-1-1-1-1-1-1-1-10000000000000000
χ8666666666-3-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000000000000-2-2-2-2000000-2-200111111110000000000000000
χ8766666666-3-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000000000002222000000-2-200-1-1-1-111110000000000000000
χ8866666666-3-3-3-3-3-3-3-3-6-6333300000000000000000000000000000000000000000000-2-2-2-200000022001111-1-1-1-10000000000000000
χ89666-6-66-6-6-3-33-333-330033−3333−33000000000000000000000000000000000000000000002-22-20000000000-11-113−33−30000000000000000
χ90666-6-66-6-6-3-33-333-330033−3333−3300000000000000000000000000000000000000000000-22-2200000000001-11-1−33−330000000000000000
χ91666-6-66-6-6-3-33-333-3300−3333−3333000000000000000000000000000000000000000000002-22-20000000000-11-11−33−330000000000000000
χ92666-6-66-6-6-3-33-333-3300−3333−333300000000000000000000000000000000000000000000-22-2200000000001-11-13−33−30000000000000000
χ9366-66-6-6-66-3-333-333-30033−33−3333000000000000000000000000000000000000000000002i−2i−2i2i0000000000−iii−ii3−i3−i3i30000000000000000
χ9466-66-6-6-66-3-333-333-30033−33−333300000000000000000000000000000000000000000000−2i2i2i−2i0000000000i−i−ii−i3i3i3−i30000000000000000
χ9566-66-6-6-66-3-333-333-300−333333−33000000000000000000000000000000000000000000002i−2i−2i2i0000000000−iii−i−i3i3i3−i30000000000000000
χ9666-66-6-6-66-3-333-333-300−333333−3300000000000000000000000000000000000000000000−2i2i2i−2i0000000000i−i−iii3−i3−i3i30000000000000000
χ9766-6-66-66-6-3-3-333-3336-6-3-333000000000000000000000000000000000000000000002i2i−2i−2i0000002i−2i00−i−iii−i−iii0000000000000000
χ9866-6-66-66-6-3-3-333-3336-6-3-33300000000000000000000000000000000000000000000−2i−2i2i2i000000−2i2i00ii−i−iii−i−i0000000000000000
χ9966-6-66-66-6-3-3-333-333-6633-3-3000000000000000000000000000000000000000000002i2i−2i−2i000000−2i2i00−i−iiiii−i−i0000000000000000
χ10066-6-66-66-6-3-3-333-333-6633-3-300000000000000000000000000000000000000000000−2i−2i2i2i0000002i−2i00ii−i−i−i−iii0000000000000000
χ10112-12121212-12-12-12-66-6-6-66660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10212-1212-12-12-121212-666-66-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-12-1212-121212-12-6666-6-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-12-12-121212-1212-66-6666-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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