Finite Group Databasebeta

← Group #13155169

Character table — Group #13155169

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1122222224488888888888888888888888899181818181818183636363636363636363636363636108108108108108108108108
order122344666121233366666666612121212121212121212121222244666644441212121212121212121288888888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111-1-1111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-11111-1-1-1-1ii−i−iii−i−i
χ61111-1-1111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-11111-1-1-1-1−i−iii−i−iii
χ71111-1-1111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-111-1-1-1-1-1-11111ii−i−i−i−iii
χ81111-1-1111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-111-1-1-1-1-1-11111−i−iiiii−i−i
χ911-111-1-1-111-1111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-111-1-1i−ii−i1-1ii−i−iii−i−i1-11-1i−ii−i
χ1011-111-1-1-111-1111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-111-1-1i−ii−i1-1ii−i−iii−i−i-11-11−ii−ii
χ1111-111-1-1-111-1111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-111-1-1−ii−ii1-1−i−iii−i−iii1-11-1−ii−ii
χ1211-111-1-1-111-1111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-111-1-1−ii−ii1-1−i−iii−i−iii-11-11i−ii−i
χ1311-11-11-1-11-11111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-11-1111-1-1i−i−ii-11ii−i−i−i−iiii−i−ii-111-1
χ1411-11-11-1-11-11111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-11-1111-1-1i−i−ii-11ii−i−i−i−iii−iii−i1-1-11
χ1511-11-11-1-11-11111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-11-1111-1-1−iii−i-11−i−iiiii−i−ii−i−ii1-1-11
χ1611-11-11-1-11-11111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-11-1111-1-1−iii−i-11−i−iiiii−i−i−iii−i-111-1
χ1722222222222222222222222222222222222-2-2-2-2-2-2-2-2-20000-2-20000000000000000
χ182222-2-2222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-20000220000000000000000
χ19222-122-1-1-1-1-12-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-122222-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000
χ20222-122-1-1-1-1-12-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-122222-1-1-1-1-2-2-2-2-1-11111111100000000
χ21222-122-1-1-1-1-12-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-1-2-2-2-2-211110000113−33−33−33−300000000
χ22222-122-1-1-1-1-12-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-1-2-2-2-2-21111000011−33−33−33−3300000000
χ23222-1-2-2-1-1-1112-1-122-1-1-1-12-1-1-2-21111-2-21111222-2-2-1-1-1-122-2-211-1-1-1-1111100000000
χ24222-1-2-2-1-1-1112-1-122-1-1-1-12-1-1-2-21111-2-21111222-2-2-1-1-1-1-2-222111111-1-1-1-100000000
χ25222-1-2-2-1-1-1112-1-122-1-1-1-12-1-1-2-21111-2-21111-2-2-22211110000-1-13−33−3−33−3300000000
χ26222-1-2-2-1-1-1112-1-122-1-1-1-12-1-1-2-21111-2-21111-2-2-22211110000-1-1−33−333−33−300000000
χ2722-222-2-2-222-2222-2-2-2-2-2-2222222222-2-2-2-2-2-222-2-22-2-2220000-220000000000000000
χ2822-22-22-2-22-22222-2-2-2-2-2-2222-2-2-2-2-2-222222222-22-2-2-22200002-20000000000000000
χ2922-2-12-211-1-112-1-1-2-211112-1-122-1-1-1-1-2-2111122-2-2211-1-100001-1−i3i3i3−i3−i3i3i3−i300000000
χ3022-2-12-211-1-112-1-1-2-211112-1-122-1-1-1-1-2-2111122-2-2211-1-100001-1i3−i3−i3i3i3−i3−i3i300000000
χ3122-2-12-211-1-112-1-1-2-211112-1-122-1-1-1-1-2-21111-2-222-2-1-1112i−2i2i−2i-11−i−iii−i−iii00000000
χ3222-2-12-211-1-112-1-1-2-211112-1-122-1-1-1-1-2-21111-2-222-2-1-111−2i2i−2i2i-11ii−i−iii−i−i00000000
χ3322-2-1-2211-11-12-1-1-2-211112-1-1-2-2111122-1-1-1-122-22-211-1-10000-11−i3i3i3−i3i3−i3−i3i300000000
χ3422-2-1-2211-11-12-1-1-2-211112-1-1-2-2111122-1-1-1-122-22-211-1-10000-11i3−i3−i3i3−i3i3i3−i300000000
χ3522-2-1-2211-11-12-1-1-2-211112-1-1-2-2111122-1-1-1-1-2-22-22-1-1112i−2i−2i2i1-1−i−iiiii−i−i00000000
χ3622-2-1-2211-11-12-1-1-2-211112-1-1-2-2111122-1-1-1-1-2-22-22-1-111−2i2i2i−2i1-1ii−i−i−i−iii00000000
χ374-4040000-400444000000-4-4-40000000000004-4000004-40000000000000000000000
χ384-4040000-400444000000-4-4-4000000000000-4400000-440000000000000000000000
χ394-40-200−2i32i32004-2-200−2i3−2i32i32i3-4220000000000004-4000−2i32i3-220000000000000000000000
χ404-40-200−2i32i32004-2-200−2i3−2i32i32i3-422000000000000-440002i3−2i32-20000000000000000000000
χ414-40-2002i3−2i32004-2-2002i32i3−2i3−2i3-4220000000000004-40002i3−2i3-220000000000000000000000
χ424-40-2002i3−2i32004-2-2002i32i3−2i3−2i3-422000000000000-44000−2i32i32-20000000000000000000000
χ4388888888888-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000000
χ448888-8-8888-8-8-1-1-1-1-1-1-1-1-1-1-1-11111111111110000000000000000000000000000000
χ45888-488-4-4-4-4-4-11−3i321+3i32-1-11−3i321+3i321−3i321+3i32-11−3i321+3i32-1-11−3i321−3i321+3i321+3i32-1-11−3i321−3i321+3i321+3i320000000000000000000000000000000
χ46888-488-4-4-4-4-4-11+3i321−3i32-1-11+3i321−3i321+3i321−3i32-11+3i321−3i32-1-11+3i321+3i321−3i321−3i32-1-11+3i321+3i321−3i321−3i320000000000000000000000000000000
χ47888-4-8-8-4-4-444-11−3i321+3i32-1-11−3i321+3i321−3i321+3i32-11−3i321+3i3211−1+3i32−1+3i32−1−3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i320000000000000000000000000000000
χ48888-4-8-8-4-4-444-11+3i321−3i32-1-11+3i321−3i321+3i321−3i32-11+3i321−3i3211−1−3i32−1−3i32−1+3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i320000000000000000000000000000000
χ4988-888-8-8-888-8-1-1-1111111-1-1-1-1-1-1-1-1-11111110000000000000000000000000000000
χ5088-88-88-8-88-88-1-1-1111111-1-1-1111111-1-1-1-1-1-10000000000000000000000000000000
χ5188-8-48-844-4-44-11−3i321+3i3211−1+3i32−1−3i32−1+3i32−1−3i32-11−3i321+3i32-1-11−3i321−3i321+3i321+3i3211−1+3i32−1+3i32−1−3i32−1−3i320000000000000000000000000000000
χ5288-8-48-844-4-44-11+3i321−3i3211−1−3i32−1+3i32−1−3i32−1+3i32-11+3i321−3i32-1-11+3i321+3i321−3i321−3i3211−1−3i32−1−3i32−1+3i32−1+3i320000000000000000000000000000000
χ5388-8-4-8844-44-4-11−3i321+3i3211−1+3i32−1−3i32−1+3i32−1−3i32-11−3i321+3i3211−1+3i32−1+3i32−1−3i32−1−3i32-1-11−3i321−3i321+3i321+3i320000000000000000000000000000000
χ5488-8-4-8844-44-4-11+3i321−3i3211−1−3i32−1+3i32−1−3i32−1+3i32-11+3i321−3i3211−1−3i32−1−3i32−1+3i32−1+3i32-1-11+3i321+3i321−3i321−3i320000000000000000000000000000000
χ558-8080000-800-1-1-13-33-3-331113i−3i3i−3i3i−3i3i−3i3i−3i3i−3i0000000000000000000000000000000
χ568-8080000-800-1-1-13-33-3-33111−3i3i−3i3i−3i3i−3i3i−3i3i−3i3i0000000000000000000000000000000
χ578-8080000-800-1-1-1-33-333-31113i−3i3i−3i3i−3i−3i3i−3i3i−3i3i0000000000000000000000000000000
χ588-8080000-800-1-1-1-33-333-3111−3i3i−3i3i−3i3i3i−3i3i−3i3i−3i0000000000000000000000000000000
χ598-80-400−4i34i3400-11−3i321+3i323-3−3+i323+i323−i32−3−i321−1+3i32−1−3i323i−3i3ζ11−3ζ113ζ7−3ζ73i−3i3ζ11−3ζ113ζ7−3ζ70000000000000000000000000000000
χ608-80-400−4i34i3400-11−3i321+3i323-3−3+i323+i323−i32−3−i321−1+3i32−1−3i32−3i3i−3ζ113ζ11−3ζ73ζ7−3i3i−3ζ113ζ11−3ζ73ζ70000000000000000000000000000000
χ618-80-400−4i34i3400-11+3i321−3i32-333+i32−3+i32−3−i323−i321−1−3i32−1+3i323i−3i3ζ7−3ζ73ζ11−3ζ11−3i3i−3ζ73ζ7−3ζ113ζ110000000000000000000000000000000
χ628-80-400−4i34i3400-11+3i321−3i32-333+i32−3+i32−3−i323−i321−1−3i32−1+3i32−3i3i−3ζ73ζ7−3ζ113ζ113i−3i3ζ7−3ζ73ζ11−3ζ110000000000000000000000000000000
χ638-80-4004i3−4i3400-11−3i321+3i32-333−i32−3−i32−3+i323+i321−1+3i32−1−3i323i−3i3ζ11−3ζ113ζ7−3ζ7−3i3i−3ζ113ζ11−3ζ73ζ70000000000000000000000000000000
χ648-80-4004i3−4i3400-11−3i321+3i32-333−i32−3−i32−3+i323+i321−1+3i32−1−3i32−3i3i−3ζ113ζ11−3ζ73ζ73i−3i3ζ11−3ζ113ζ7−3ζ70000000000000000000000000000000
χ658-80-4004i3−4i3400-11+3i321−3i323-3−3−i323−i323+i32−3+i321−1−3i32−1+3i323i−3i3ζ7−3ζ73ζ11−3ζ113i−3i3ζ7−3ζ73ζ11−3ζ110000000000000000000000000000000
χ668-80-4004i3−4i3400-11+3i321−3i323-3−3−i323−i323+i32−3+i321−1−3i32−1+3i32−3i3i−3ζ73ζ7−3ζ113ζ11−3i3i−3ζ73ζ7−3ζ113ζ110000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.