Finite Group Databasebeta

← Group #13167457

Character table — Group #13167457

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222244444444444444888888888888888888181818181818181836363636363636363636363636363636363636363636363636363636363672727272
order12442346121233666661212121212121233666666612121212121212121222446612126888888888888122424242424242424242424242424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111-11-111111-1-1-111-1-1-1111111-1-1-1-1-111-11111-1-1-1-11-1-111111-111-1-111-1-111-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111-11-111111-1-1-111-1-1-1111111-1-1-1-1-111-11111-1-1-1-11-1-111111-111-1-1-1-111-1-111-11111-1-1-1-1-1-1-1-11111-1-111
χ71111-11-111111-1-1-111-1-1-1111111-1-1-1-1-111-11111-1-1-1-11-1-111111-1-1-11111-1-1-1-111-1-1-1-1-11111-1-1-1-1111111-1-1
χ81111-11-111111-1-1-111-1-1-1111111-1-1-1-1-111-11111-1-1-1-11-1-111111-1-1-111-1-11111-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ911-1-111-11-1-11111111-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1i−ii−ii−ii−i1-11-11ii−i−iii−i−i11-1-111-1-1i−ii−i
χ1011-1-111-11-1-11111111-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1i−ii−i−ii−ii-11-111ii−i−iii−i−i-1-111-1-111−ii−ii
χ1111-1-111-11-1-11111111-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1−ii−iii−ii−i-11-111−i−iii−i−iii-1-111-1-111i−ii−i
χ1211-1-111-11-1-11111111-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1−ii−ii−ii−ii1-11-11−i−iii−i−iii11-1-111-1-1−ii−ii
χ1311-1-1-1111-1-111-1-1-111111-1-1-1-111-1-1-1-1-1111-1-1-1-11111-11-11-1-1111i−i−iii−i−ii1-1-11-1ii−i−i−i−iii11-1-1-1-111i−i−ii
χ1411-1-1-1111-1-111-1-1-111111-1-1-1-111-1-1-1-1-1111-1-1-1-11111-11-11-1-1111i−i−ii−iii−i-111-1-1ii−i−i−i−iii-1-11111-1-1−iii−i
χ1511-1-1-1111-1-111-1-1-111111-1-1-1-111-1-1-1-1-1111-1-1-1-11111-11-11-1-1111−iii−ii−i−ii-111-1-1−i−iiiii−i−i-1-11111-1-1i−i−ii
χ1611-1-1-1111-1-111-1-1-111111-1-1-1-111-1-1-1-1-1111-1-1-1-11111-11-11-1-1111−iii−i−iii−i1-1-11-1−i−iiiii−i−i11-1-1-1-111−iii−i
χ17222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2000000000000-200000000000000000000
χ1822222-12-1-1-122-12222-1222222-1-12-1-1-1-1-1-12-1-1-1-1-1-1-1-12222-1-1-1-1-1000000002222-100000000-1-1-1-1-1-1-1-10000
χ1922222-12-1-1-122-12222-1222222-1-12-1-1-1-1-1-12-1-1-1-1-1-1-1-12222-1-1-1-1-100000000-2-2-2-2-100000000111111110000
χ2022222-12-1-1-122-12222-1222222-1-12-1-1-1-1-1-12-1-1-1-1-1-1-1-1-2-2-2-2111110000000000001000000003−33−33−33−30000
χ2122222-12-1-1-122-12222-1222222-1-12-1-1-1-1-1-12-1-1-1-1-1-1-1-1-2-2-2-211111000000000000100000000−33−33−33−330000
χ222222-22-222222-2-2-222-2-2-2222222-2-2-2-2-222-22222-2-2-2-2-222-2-2-2-2-22000000000000200000000000000000000
χ232222-2-1-2-1-1-1221-2-2221-2-22222-1-1-21111-1-1-2-1-1-1-111112-2-22-1-1-1-110000000022-2-2100000000-1-1-1-111110000
χ242222-2-1-2-1-1-1221-2-2221-2-22222-1-1-21111-1-1-2-1-1-1-111112-2-22-1-1-1-1100000000-2-2221000000001111-1-1-1-10000
χ252222-2-1-2-1-1-1221-2-2221-2-22222-1-1-21111-1-1-2-1-1-1-11111-222-21111-1000000000000-1000000003−33−3−33−330000
χ262222-2-1-2-1-1-1221-2-2221-2-22222-1-1-21111-1-1-2-1-1-1-11111-222-21111-1000000000000-100000000−33−333−33−30000
χ2722-2-222-22-2-22222222-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-222-2-222-2-22000000000000-200000000000000000000
χ2822-2-22-1-2-11122-122221-2-2-2-2-2-2-1-12-1-1-1-1-1-1-21111111122-2-2-1-111-10000000000001000000003−3−333−3−330000
χ2922-2-22-1-2-11122-122221-2-2-2-2-2-2-1-12-1-1-1-1-1-1-21111111122-2-2-1-111-1000000000000100000000−333−3−333−30000
χ3022-2-22-1-2-11122-122221-2-2-2-2-2-2-1-12-1-1-1-1-1-1-211111111-2-22211-1-11000000002-22-2-100000000-1-111-1-1110000
χ3122-2-22-1-2-11122-122221-2-2-2-2-2-2-1-12-1-1-1-1-1-1-211111111-2-22211-1-1100000000-22-22-10000000011-1-111-1-10000
χ3222-2-2-2222-2-222-2-2-222222-2-2-2-222-2-2-2-2-2222-2-2-2-222222-22-222-2-2-2000000000000200000000000000000000
χ3322-2-2-2-12-111221-2-222-122-2-2-2-2-1-1-21111-1-121111-1-1-1-12-22-2-1-1111000000000000-1000000003−3−33−333−30000
χ3422-2-2-2-12-111221-2-222-122-2-2-2-2-1-1-21111-1-121111-1-1-1-12-22-2-1-1111000000000000-100000000−333−33−3−330000
χ3522-2-2-2-12-111221-2-222-122-2-2-2-2-1-1-21111-1-121111-1-1-1-1-22-2211-1-1-1000000002-2-22100000000-1-11111-1-10000
χ3622-2-2-2-12-111221-2-222-122-2-2-2-2-1-1-21111-1-121111-1-1-1-1-22-2211-1-1-100000000-222-210000000011-1-1-1-1110000
χ3744444444441-24111-241111-2-21-2-211-2-21-2-211-2-211-2-20000000002222000000000-1-1-1-1-1-1-1-1000000000000
χ3844444444441-24111-241111-2-21-2-211-2-21-2-211-2-211-2-2000000000-2-2-2-200000000011111111000000000000
χ394444444444-214-2-2-214-2-2-2-211-211-2-211-211-2-211-2-21100000000000002222000000000000000000000-1-1-1-1
χ404444444444-214-2-2-214-2-2-2-211-211-2-211-211-2-211-2-2110000000000000-2-2-2-20000000000000000000001111
χ414444-44-44441-2-4-1-11-2-4-1-111-2-21-22-1-1221-2211-2-2-1-12200000000022-2-2000000000-1-1-1-11111000000000000
χ424444-44-44441-2-4-1-11-2-4-1-111-2-21-22-1-1221-2211-2-2-1-122000000000-2-2220000000001111-1-1-1-1000000000000
χ434444-44-4444-21-422-21-422-2-211-21-122-1-1-21-1-2-21122-1-1000000000000022-2-2000000000000000000000-1-111
χ444444-44-4444-21-422-21-422-2-211-21-122-1-1-21-1-2-21122-1-10000000000000-2-22200000000000000000000011-1-1
χ4544-4-444-44-4-41-24111-2-4-1-1-1-1221-2-211-2-21-22-1-122-1-1220000000002i−2i2i−2i000000000−i−iii−i−iii000000000000
χ4644-4-444-44-4-41-24111-2-4-1-1-1-1221-2-211-2-21-22-1-122-1-122000000000−2i2i−2i2i000000000ii−i−iii−i−i000000000000
χ4744-4-444-44-4-4-214-2-2-21-42222-1-1-211-2-211-21-122-1-122-1-100000000000002i−2i2i−2i000000000000000000000−ii−ii
χ4844-4-444-44-4-4-214-2-2-21-42222-1-1-211-2-211-21-122-1-122-1-10000000000000−2i2i−2i2i000000000000000000000i−ii−i
χ4944-4-4-4444-4-41-2-4-1-11-2411-1-1221-22-1-1221-2-2-1-12211-2-20000000002i−2i−2i2i000000000−i−iiiii−i−i000000000000
χ5044-4-4-4444-4-41-2-4-1-11-2411-1-1221-22-1-1221-2-2-1-12211-2-2000000000−2i2i2i−2i000000000ii−i−i−i−iii000000000000
χ5144-4-4-4444-4-4-21-422-214-2-222-1-1-21-122-1-1-21122-1-1-2-21100000000000002i−2i−2i2i000000000000000000000−iii−i
χ5244-4-4-4444-4-4-21-422-214-2-222-1-1-21-122-1-1-21122-1-1-2-2110000000000000−2i2i2i−2i000000000000000000000i−i−ii
χ534-44i−4i040-44i−4i1-203-3-1203i−3ii−i2i−2i1-203-300-120i−i2i−2i3i−3i000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000
χ544-44i−4i040-44i−4i1-203-3-1203i−3ii−i2i−2i1-203-300-120i−i2i−2i3i−3i000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000
χ554-44i−4i040-44i−4i1-20-33-120−3i3ii−i2i−2i1-20-3300-120i−i2i−2i−3i3i000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000
χ564-44i−4i040-44i−4i1-20-33-120−3i3ii−i2i−2i1-20-3300-120i−i2i−2i−3i3i000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000
χ574-44i−4i040-44i−4i44000-4-40004i−4i−4i4i4400000-4-404i−4i−4i4i0000000000000000000000000000000000000000000000
χ584-44i−4i0-202−2i2i44000-4-40004i−4i−4i4i-2-200000220−2i2i2i−2i00000000−2i32i323−230000000000000000000000000000000000
χ594-44i−4i0-202−2i2i44000-4-40004i−4i−4i4i-2-200000220−2i2i2i−2i000000002i3−2i3−23230000000000000000000000000000000000
χ604-4−4i4i040-4−4i4i1-203-3-120−3i3i−ii−2i2i1-203-300-120−ii−2i2i−3i3i000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000
χ614-4−4i4i040-4−4i4i1-203-3-120−3i3i−ii−2i2i1-203-300-120−ii−2i2i−3i3i000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000
χ624-4−4i4i040-4−4i4i1-20-33-1203i−3i−ii−2i2i1-20-3300-120−ii−2i2i3i−3i000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000
χ634-4−4i4i040-4−4i4i1-20-33-1203i−3i−ii−2i2i1-20-3300-120−ii−2i2i3i−3i000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000
χ644-4−4i4i040-4−4i4i44000-4-4000−4i4i4i−4i4400000-4-40−4i4i4i−4i0000000000000000000000000000000000000000000000
χ654-4−4i4i0-2022i−2i44000-4-4000−4i4i4i−4i-2-2000002202i−2i−2i2i00000000−2i32i3−23230000000000000000000000000000000000
χ664-4−4i4i0-2022i−2i44000-4-4000−4i4i4i−4i-2-2000002202i−2i−2i2i000000002i3−2i323−230000000000000000000000000000000000
χ6788888-48-4-4-42-4-4222-4-42222-4-4-12-4-1-122-12-4-1-122-1-122000000000000000000000000000000000000000000
χ6888888-48-4-4-4-42-4-4-4-42-4-4-4-4-4222-1222-1-12-1222-1-122-1-1000000000000000000000000000000000000000000
χ698888-8-4-8-4-4-42-44-2-22-44-2-222-4-4-12411-2-2-124-1-12211-2-2000000000000000000000000000000000000000000
χ708888-8-4-8-4-4-4-42444-42444-4-4222-1-2-2-2112-1-222-1-1-2-211000000000000000000000000000000000000000000
χ7188-8-88-4-8-4442-4-4222-44-2-2-2-244-12-4-1-122-12411-2-211-2-2000000000000000000000000000000000000000000
χ7288-8-88-4-8-444-42-4-4-4-4244444-2-22-1222-1-12-1-2-2-211-2-211000000000000000000000000000000000000000000
χ7388-8-8-8-48-4442-44-2-22-4-422-2-244-12411-2-2-12-411-2-2-1-122000000000000000000000000000000000000000000
χ7488-8-8-8-48-444-42444-42-4-4-444-2-22-1-2-2-2112-12-2-21122-1-1000000000000000000000000000000000000000000
χ758-88i−8i080-88i−8i-420004-2000−4i4i−2i2i-42000004-20−4i4i−2i2i0000000000000000000000000000000000000000000000
χ768-88i−8i0-404−4i4i2-406-6-2406i−6i2i−2i4i−4i-120-33001-20−ii−2i2i−3i3i00000000000000000000000000000000000000000000
χ778-88i−8i0-404−4i4i2-40-66-240−6i6i2i−2i4i−4i-1203-3001-20−ii−2i2i3i−3i00000000000000000000000000000000000000000000
χ788-88i−8i0-404−4i4i-420004-2000−4i4i−2i2i2-1000−3i33i3-2102i−2ii−i0033−33000000000000000000000000000000000000000000
χ798-88i−8i0-404−4i4i-420004-2000−4i4i−2i2i2-10003i3−3i3-2102i−2ii−i00−3333000000000000000000000000000000000000000000
χ808-8−8i8i080-8−8i8i-420004-20004i−4i2i−2i-42000004-204i−4i2i−2i0000000000000000000000000000000000000000000000
χ818-8−8i8i0-4044i−4i2-406-6-240−6i6i−2i2i−4i4i-120-33001-20i−i2i−2i3i−3i00000000000000000000000000000000000000000000
χ828-8−8i8i0-4044i−4i2-40-66-2406i−6i−2i2i−4i4i-1203-3001-20i−i2i−2i−3i3i00000000000000000000000000000000000000000000
χ838-8−8i8i0-4044i−4i-420004-20004i−4i2i−2i2-1000−3i33i3-210−2i2i−ii00−3333000000000000000000000000000000000000000000
χ848-8−8i8i0-4044i−4i-420004-20004i−4i2i−2i2-10003i3−3i3-210−2i2i−ii0033−33000000000000000000000000000000000000000000

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