Finite Group Databasebeta

← Group #13151930

Character table — Group #13151930

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1122222222244444446666661212121212121212121212121212121212181818181818242424242424363636363636363636363636363636363636363636363636363636363636363636
order122223444466661212121233661212366666661212121212121212128824242424666121212224444446666888121212121212121212121212242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ311111111111111111111111111111111111111111-1-1-1-1-1-11111111-1111-1-1-111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1111111-11-1-1-1111-1-111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ5111-1-111-1-1111-1-111-1-111111111-1-11-1-111-1-111-1-1111111111-1-11-1-1111-1-11-1-111111-1-111-1-1-1-111-1-1-1-111-1-1-1-1
χ6111-1-111-1-1111-1-111-1-111111111-1-11-1-111-1-111-1-1111111111-1-11-1-1-1-1-111-111-1-1-1-11-1-1-1-11111-1-1111111-1-1-1-1
χ7111-1-111-1-1111-1-111-1-111111111-1-11-1-111-1-111-1-111-1-1-1-1-1-11-1-11-1-11-11-1-1-11111-1-1-11111-1-1-1-1-1-11111-1-11111
χ8111-1-111-1-1111-1-111-1-111111111-1-11-1-111-1-111-1-111-1-1-1-1-1-11-1-11-1-1-11-1111-1-1-1-111-111-1-1111111-1-1-1-1-1-11111
χ911-11-11-11-111-11-11-11-11111111-11-1-11-11-11-11-11-111111111-11-1-11-111-11-1-11-11111-11-1-1-111-1-1-1-111-1-1-1-111-1-1
χ1011-11-11-11-111-11-11-11-11111111-11-1-11-11-11-11-11-111111111-11-1-11-1-1-11-111-11-1-1-1-1-11-111-1-11111-1-111-1-111-1-1
χ1111-11-11-11-111-11-11-11-11111111-11-1-11-11-11-11-11-111-1-1-1-1-1-1-11-1-11-11-1-11-11-1111-1-11-11-1-111-1-111-1-11111-1-111
χ1211-11-11-11-111-11-11-11-11111111-11-1-11-11-11-11-11-111-1-1-1-1-1-1-11-1-11-1-111-11-11-1-1-1111-1111-1-111-1-111-1-111-1-111
χ1311-1-111-1-1111-1-111-1-111111111-1-11-1-111-1-111-1-1111111111-1-11-1-1111-1-11-1-111111-1-11-1-1-1-111-1-1-1-111-1-1-1-111
χ1411-1-111-1-1111-1-111-1-111111111-1-11-1-111-1-111-1-1111111111-1-11-1-11-1-111-111-1-1-1-1-1-1-111111-1-11111-1-1-1-1-1-111
χ1511-1-111-1-1111-1-111-1-111111111-1-11-1-111-1-111-1-1111-1-1-1-1-1-1-1-11-1-111-1-1-1111-111-1-111-1-1-1-1-1111111-1-11111-1-1
χ1611-1-111-1-1111-1-111-1-111111111-1-11-1-111-1-111-1-1111-1-1-1-1-1-1-1-11-1-11-1111-1-1-11-1-11111-11111-1-1-1-1-1-1111111-1-1
χ172222222222222222222-12-122-1222-1-1-1-1222-1-1-1-1-1-1000000-1-1-1-1-1-10200022200-1-1000000000-1-1-1-1-1-1000000
χ182222222222222222222-12-122-1222-1-1-1-1222-1-1-1-1-1-1000000-1-1-1-1-1-10-2000-2-2-20011000000000111111000000
χ19222222222222222222-12-12-1-1-1-1-1-1222-1-1-1-12222-1-122-1-1-1-1-1-1-1-1-1-1000000000000222000000000000-1-1-1-1-1-1
χ20222222222222222222-12-12-1-1-1-1-1-1222-1-1-1-12222-1-1-2-21111-1-1-1-1-1-1000000000000-2-2-2000000000000111111
χ212222-22-2-22-2222-2-2-2-222222-2-2222-222-22-2-22-2-2-22-2-200000022-2-2-22000000000000000000000000000000000
χ222222-22-2-22-2222-2-2-2-222-12-1-2-2-122-2-1-11-1-2-22111-111000000-1-1111-10000000000−i3i3000000000−i3i3−i3i3−i3i3000000
χ232222-22-2-22-2222-2-2-2-222-12-1-2-2-122-2-1-11-1-2-22111-111000000-1-1111-10000000000i3−i3000000000i3−i3i3−i3i3−i3000000
χ242222-22-2-22-2222-2-2-2-22-12-1211-1-1-1122-2-111-1-2-2-22110033−3−3-1-1111-10000000000000000000000000003−33−33−3
χ252222-22-2-22-2222-2-2-2-22-12-1211-1-1-1122-2-111-1-2-2-221100−3−333-1-1111-1000000000000000000000000000−33−33−33
χ26222-222-22-2-222-22-2-22-22222-2-222-222-222-22-2-2-22-2-2-20000002-22-22-2000000000000000000000000000000000
χ27222-222-22-2-222-22-2-22-22-12-1-2-2-12-22-11-1-1-22-211-1111000000-11-11-110000000000−i3i3000000000−i3i3i3−i3i3−i3000000
χ28222-222-22-2-222-22-2-22-22-12-1-2-2-12-22-11-1-1-22-211-1111000000-11-11-110000000000i3−i3000000000i3−i3−i3i3−i3i3000000
χ29222-222-22-2-222-22-2-22-2-12-1211-1-11-12-22-11-11-2-22-2110033−3−3-11-11-110000000000000000000000000003−3−33−33
χ30222-222-22-2-222-22-2-22-2-12-1211-1-11-12-22-11-11-2-22-21100−3−333-11-11-11000000000000000000000000000−333−33−3
χ31222-2-222-2-2222-2-222-2-22-12-122-12-2-2-111-12-2-2-1-111-1-1000000-111-111020002-2-200-1-1000000000-1-11111000000
χ32222-2-222-2-2222-2-222-2-22-12-122-12-2-2-111-12-2-2-1-111-1-1000000-111-1110-2000-222001100000000011-1-1-1-1000000
χ33222-2-222-2-2222-2-222-2-2-12-12-1-1-1-1112-2-2-1-11122-2-2-1-122-1-1-1-1-111-1110000000000002-2-2000000000000-1-11111
χ34222-2-222-2-2222-2-222-2-2-12-12-1-1-1-1112-2-2-1-11122-2-2-1-1-2-21111-111-111000000000000-22200000000000011-1-1-1-1
χ3522-22222-2-2-22-222-22-2-22222-2-22-222-22222-2-2-22-2-2-2-2000000-2222-2-2000000000000000000000000000000000
χ3622-22222-2-2-22-222-22-2-22-12-1-2-2-1-2221-1-1-12-2-21-111110000001-1-1-1110000000000−i3i3000000000i3−i3−i3i3i3−i3000000
χ3722-22222-2-2-22-222-22-2-22-12-1-2-2-1-2221-1-1-12-2-21-111110000001-1-1-1110000000000i3−i3000000000−i3i3i3−i3−i3i3000000
χ3822-22222-2-2-22-222-22-2-2-12-1211-11-1-1-222-1-111-22-2-2110033−3−31-1-1-111000000000000000000000000000−333−3−33
χ3922-22222-2-2-22-222-22-2-2-12-1211-11-1-1-222-1-111-22-2-21100−3−3331-1-1-1110000000000000000000000000003−3−333−3
χ4022-22-22-22-222-22-22-22-22-12-122-1-22-21-11-1-22-2-11-11-1-10000001-111-1102000-22-200-1-100000000011-1-111000000
χ4122-22-22-22-222-22-22-22-22-12-122-1-22-21-11-1-22-2-11-11-1-10000001-111-110-20002-220011000000000-1-111-1-1000000
χ4222-22-22-22-222-22-22-22-2-12-12-1-1-11-11-22-2-11-112-22-2-1-122-1-1-1-11-111-11000000000000-22-200000000000011-1-111
χ4322-22-22-22-222-22-22-22-2-12-12-1-1-11-11-22-2-11-112-22-2-1-1-2-211111-111-110000000000002-22000000000000-1-111-1-1
χ4422-2-222-2-2222-2-222-2-222-12-122-1-2-2211-1-1-2-22-111-1-1-100000011-111-102000-2-2200-1-10000000001111-1-1000000
χ4522-2-222-2-2222-2-222-2-222-12-122-1-2-2211-1-1-2-22-111-1-1-100000011-111-10-200022-20011000000000-1-1-1-111000000
χ4622-2-222-2-2222-2-222-2-22-12-12-1-1-111-1-2-22-111-12-2-22-1-122-1-1-1-111-111-1000000000000-2-220000000000001111-1-1
χ4722-2-222-2-2222-2-222-2-22-12-12-1-1-111-1-2-22-111-12-2-22-1-1-2-2111111-111-100000000000022-2000000000000-1-1-1-111
χ4822-2-2-22222-22-2-2-2-22222222-2-22-2-2-2-2-2-22222-2222-2-2000000-2-2-2222000000000000000000000000000000000
χ4922-2-2-22222-22-2-2-2-22222-12-1-2-2-1-2-2-2111-12221-1-1-111000000111-1-1-10000000000−i3i3000000000i3−i3i3−i3−i3i3000000
χ5022-2-2-22222-22-2-2-2-22222-12-1-2-2-1-2-2-2111-12221-1-1-111000000111-1-1-10000000000i3−i3000000000−i3i3−i3i3i3−i3000000
χ5122-2-2-22222-22-2-2-2-2222-12-1211-1111-2-2-2-1-1-1-1-2222110033−3−3111-1-1-1000000000000000000000000000−33−333−3
χ5222-2-2-22222-22-2-2-2-2222-12-1211-1111-2-2-2-1-1-1-1-22221100−3−333111-1-1-10000000000000000000000000003−33−3−33
χ53444444444444444444-2-2-2-2-2-21-2-2-2-2-2-21-2-2-2-2-2-2-211000000111111000000000000000000000000000000000
χ544444-44-4-44-4444-4-4-4-44-2-2-2-2221-2-22-2-22122-2222-2-1-100000011-1-1-11000000000000000000000000000000000
χ55444-444-44-4-444-44-4-44-4-2-2-2-2221-22-2-22-212-2222-22-1-10000001-11-11-1000000000000000000000000000000000
χ56444-4-444-4-4444-4-444-4-4-2-2-2-2-2-21-222-2221-222-2-222110000001-1-11-1-1000000000000000000000000000000000
χ5744-44444-4-4-44-444-44-4-4-2-2-2-22212-2-22-2-21-2222-222-1-1000000-1111-1-1000000000000000000000000000000000
χ5844-44-44-44-444-44-44-44-4-2-2-2-2-2-212-222-2212-22-22-2211000000-11-1-11-1000000000000000000000000000000000
χ5944-4-444-4-4444-4-444-4-44-2-2-2-2-2-2122-222-2122-2-222-211000000-1-11-1-11000000000000000000000000000000000
χ6044-4-4-44444-44-4-4-4-4444-2-2-2-22212222221-2-2-22-2-2-2-1-1000000-1-1-1111000000000000000000000000000000000
χ614-400040000-4000000044-4-4004000000-400000000022−2222−2222−22000000000000000000000000000000000000000
χ624-400040000-4000000044-4-4004000000-4000000000−2222−2222−2222000000000000000000000000000000000000000
χ634-400040000-40000000-242-423−23-20000002000000023−2322−222ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23000000000000000000000000000000000000000
χ644-400040000-40000000-242-423−23-20000002000000023−23−2222−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23000000000000000000000000000000000000000
χ654-400040000-40000000-242-4−2323-200000020000000−232322−222ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7000000000000000000000000000000000000000
χ664-400040000-40000000-242-4−2323-200000020000000−2323−2222−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7000000000000000000000000000000000000000
χ6766666-36666-3-3-3-3-3-3-3-30000000000000000000000000000000000020222000-1-100000-1-1-1-1-1-1000000000000
χ6866666-36666-3-3-3-3-3-3-3-300000000000000000000000000000000000-20-2-2-20001100000111111000000000000
χ696666-6-3-6-66-6-3-3-33333-30000000000000000000000000000000000000000000−i3i300000−i3i3−i3i3−i3i3000000000000
χ706666-6-3-6-66-6-3-3-33333-30000000000000000000000000000000000000000000i3−i300000i3−i3i3−i3i3−i3000000000000
χ71666-66-3-66-6-6-3-33-333-330000000000000000000000000000000000000000000−i3i300000−i3i3i3−i3i3−i3000000000000
χ72666-66-3-66-6-6-3-33-333-330000000000000000000000000000000000000000000i3−i300000i3−i3−i3i3−i3i3000000000000
χ73666-6-6-36-6-66-3-333-3-33300000000000000000000000000000000000202-2-2000-1-100000-1-11111000000000000
χ74666-6-6-36-6-66-3-333-3-33300000000000000000000000000000000000-20-222000110000011-1-1-1-1000000000000
χ7566-666-36-6-6-6-33-3-33-3330000000000000000000000000000000000000000000−i3i300000i3−i3−i3i3i3−i3000000000000
χ7666-666-36-6-6-6-33-3-33-3330000000000000000000000000000000000000000000i3−i300000−i3i3i3−i3−i3i3000000000000
χ7766-66-6-3-66-66-33-33-33-330000000000000000000000000000000000020-22-2000-1-10000011-1-111000000000000
χ7866-66-6-3-66-66-33-33-33-3300000000000000000000000000000000000-202-220001100000-1-111-1-1000000000000
χ7966-6-66-3-6-666-333-3-333-30000000000000000000000000000000000020-2-22000-1-1000001111-1-1000000000000
χ8066-6-66-3-6-666-333-3-333-300000000000000000000000000000000000-2022-20001100000-1-1-1-111000000000000
χ8166-6-6-6-3666-6-33333-3-3-30000000000000000000000000000000000000000000−i3i300000i3−i3i3−i3−i3i3000000000000
χ8266-6-6-6-3666-6-33333-3-3-30000000000000000000000000000000000000000000i3−i300000−i3i3−i3i3i3−i3000000000000
χ838-800080000-800000008-4-8400-40000004000000000000000000000000000000000000000000000000000000
χ848-800080000-80000000-4-44443−432000000-20000000−2323000000000000000000000000000000000000000000000
χ858-800080000-80000000-4-444−43432000000-2000000023−23000000000000000000000000000000000000000000000
χ8624-24000-12000012000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.