Finite Group Databasebeta

← Group #13155170

Character table — Group #13155170

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1122222224488888888888888888888888899181818181818183636363636363636363636363636108108108108108108108108
order12234461212612333666666666121212121212121212121212222446612126888812242424242424242444448888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111-1-11-1-11-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-11ii−i−i-1iiii−i−i−i−i11-1-1ii−i−i
χ61111-1-11-1-11-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-11ii−i−i-1iiii−i−i−i−i-1-111−i−iii
χ71111-1-11-1-11-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-11−i−iii-1−i−i−i−iiiii11-1-1−i−iii
χ81111-1-11-1-11-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-11−i−iii-1−i−i−i−iiiii-1-111ii−i−i
χ911-111-1111-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11-11-1-1-1-11i−ii−i1ii−i−iii−i−ii−ii−i1-11-1
χ1011-111-1111-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11-11-1-1-1-11i−ii−i1ii−i−iii−i−i−ii−ii-11-11
χ1111-111-1111-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11-11-1-1-1-11−ii−ii1−i−iii−i−iiii−ii−i-11-11
χ1211-111-1111-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11-11-1-1-1-11−ii−ii1−i−iii−i−iii−ii−ii1-11-1
χ1311-11-111-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-111-1-1-11111-1-11-111-1-1-1-111i−i−ii−iii−i
χ1411-11-111-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-111-1-1-11111-1-11-111-1-1-1-111−iii−ii−i−ii
χ1511-11-111-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-111-1-1-1111-111-1-1-1-11111-1-1i−i−iii−i−ii
χ1611-11-111-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-111-1-1-1111-111-1-1-1-11111-1-1−iii−i−iii−i
χ1722222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-20000-20000000000000000
χ182222-2-22-2-22-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2000020000000000000000
χ19222-122-1-1-1-1-12-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-122222-1-1-1-1-12222-1-1-1-1-1-1-1-1-100000000
χ20222-122-1-1-1-1-12-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-122222-1-1-1-1-1-2-2-2-2-11111111100000000
χ21222-122-1-1-1-1-12-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-1-2-2-2-2-211111000013−33−33−33−300000000
χ22222-122-1-1-1-1-12-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-1-2-2-2-2-21111100001−33−33−33−3300000000
χ23222-1-2-2-111-112-1-122-1-1-1-12-1-1-2-21111-2-21111222-2-2-1-111-12i2i−2i−2i1−i−i−i−iiiii00000000
χ24222-1-2-2-111-112-1-122-1-1-1-12-1-1-2-21111-2-21111222-2-2-1-111-1−2i−2i2i2i1iiii−i−i−i−i00000000
χ25222-1-2-2-111-112-1-122-1-1-1-12-1-1-2-21111-2-21111-2-2-22211-1-110000-1−i3i3−i3i3i3−i3i3−i300000000
χ26222-1-2-2-111-112-1-122-1-1-1-12-1-1-2-21111-2-21111-2-2-22211-1-110000-1i3−i3i3−i3−i3i3−i3i300000000
χ2722-222-2222-2-2222-2-2-2-2-2-2222222222-2-2-2-2-2-222-22-22222-20000-20000000000000000
χ2822-22-222-2-2-22222-2-2-2-2-2-2222-2-2-2-2-2-222222222-2-2222-2-2-2000020000000000000000
χ2922-2-12-2-1-1-1112-1-1-2-211112-1-122-1-1-1-1-2-2111122-22-2-1-1-1-1100001−i3i3i3−i3−i3i3i3−i300000000
χ3022-2-12-2-1-1-1112-1-1-2-211112-1-122-1-1-1-1-2-2111122-22-2-1-1-1-1100001i3−i3−i3i3i3−i3−i3i300000000
χ3122-2-12-2-1-1-1112-1-1-2-211112-1-122-1-1-1-1-2-21111-2-22-221111-12i−2i2i−2i-1−i−iii−i−iii00000000
χ3222-2-12-2-1-1-1112-1-1-2-211112-1-122-1-1-1-1-2-21111-2-22-221111-1−2i2i−2i2i-1ii−i−iii−i−i00000000
χ3322-2-1-22-1111-12-1-1-2-211112-1-1-2-2111122-1-1-1-122-2-22-1-11110000-13−3−33−333−300000000
χ3422-2-1-22-1111-12-1-1-2-211112-1-1-2-2111122-1-1-1-122-2-22-1-11110000-1−333−33−3−3300000000
χ3522-2-1-22-1111-12-1-1-2-211112-1-1-2-2111122-1-1-1-1-2-222-211-1-1-12-2-221-1-11111-1-100000000
χ3622-2-1-22-1111-12-1-1-2-211112-1-1-2-2111122-1-1-1-1-2-222-211-1-1-1-222-2111-1-1-1-11100000000
χ374-40400-40000444000000-4-4-40000000000004-40004-4000000000000000000000000
χ384-40400-40000444000000-4-4-4000000000000-44000-44000000000000000000000000
χ394-40-200223−23004-2-2000000-422002323−23−230000004-4000-2223−230000000000000000000000
χ404-40-200223−23004-2-2000000-422002323−23−23000000-440002-2−23230000000000000000000000
χ414-40-2002−2323004-2-2000000-42200−23−2323230000004-4000-22−23230000000000000000000000
χ424-40-2002−2323004-2-2000000-42200−23−232323000000-440002-223−230000000000000000000000
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
χ448888-8-88-8-88-8-1-1-1-1-1-1-1-1-1-1-1-11111111111110000000000000000000000000000000
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
χ47888-4-8-8-444-44-11−3i321+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
χ48888-4-8-8-444-44-11+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
χ4988-888-8888-8-8-1-1-1111111-1-1-1-1-1-1-1-1-11111110000000000000000000000000000000
χ5088-88-888-8-8-88-1-1-1111111-1-1-1111111-1-1-1-1-1-10000000000000000000000000000000
χ5188-8-48-8-4-4-444-11−3i321+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
χ5288-8-48-8-4-4-444-11+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
χ5388-8-4-88-4444-4-11−3i321+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
χ5488-8-4-88-4444-4-11+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
χ558-80800-80000-1-1-13-33-33-31113i−3i3i−3i−3i3i3i−3i3i−3i3i−3i0000000000000000000000000000000
χ568-80800-80000-1-1-13-33-33-3111−3i3i−3i3i3i−3i−3i3i−3i3i−3i3i0000000000000000000000000000000
χ578-80800-80000-1-1-1-33-33-331113i−3i3i−3i−3i3i−3i3i−3i3i−3i3i0000000000000000000000000000000
χ588-80800-80000-1-1-1-33-33-33111−3i3i−3i3i3i−3i3i−3i3i−3i3i−3i0000000000000000000000000000000
χ598-80-400443−4300-11−3i321+3i323-3−3−3i323+3i32−3+3i323−3i321−1+3i32−1−3i323i−3i2ζ7+ζ11−ζ7−2ζ11−2ζ7−ζ11ζ7+2ζ113i−3i3ζ11−3ζ113ζ7−3ζ70000000000000000000000000000000
χ608-80-400443−4300-11−3i321+3i32-333+3i32−3−3i323−3i32−3+3i321−1+3i32−1−3i323i−3i2ζ7+ζ11−ζ7−2ζ11−2ζ7−ζ11ζ7+2ζ11−3i3i−3ζ113ζ11−3ζ73ζ70000000000000000000000000000000
χ618-80-400443−4300-11+3i321−3i323-3−3+3i323−3i32−3−3i323+3i321−1−3i32−1+3i32−3i3i−ζ7−2ζ112ζ7+ζ11ζ7+2ζ11−2ζ7−ζ11−3i3i−3ζ73ζ7−3ζ113ζ110000000000000000000000000000000
χ628-80-400443−4300-11+3i321−3i32-333−3i32−3+3i323+3i32−3−3i321−1−3i32−1+3i32−3i3i−ζ7−2ζ112ζ7+ζ11ζ7+2ζ11−2ζ7−ζ113i−3i3ζ7−3ζ73ζ11−3ζ110000000000000000000000000000000
χ638-80-4004−434300-11−3i321+3i323-3−3−3i323+3i32−3+3i323−3i321−1+3i32−1−3i32−3i3i−2ζ7−ζ11ζ7+2ζ112ζ7+ζ11−ζ7−2ζ11−3i3i−3ζ113ζ11−3ζ73ζ70000000000000000000000000000000
χ648-80-4004−434300-11−3i321+3i32-333+3i32−3−3i323−3i32−3+3i321−1+3i32−1−3i32−3i3i−2ζ7−ζ11ζ7+2ζ112ζ7+ζ11−ζ7−2ζ113i−3i3ζ11−3ζ113ζ7−3ζ70000000000000000000000000000000
χ658-80-4004−434300-11+3i321−3i323-3−3+3i323−3i32−3−3i323+3i321−1−3i32−1+3i323i−3iζ7+2ζ11−2ζ7−ζ11−ζ7−2ζ112ζ7+ζ113i−3i3ζ7−3ζ73ζ11−3ζ110000000000000000000000000000000
χ668-80-4004−434300-11+3i321−3i32-333−3i32−3+3i323+3i32−3−3i321−1−3i32−1+3i323i−3iζ7+2ζ11−2ζ7−ζ11−ζ7−2ζ112ζ7+ζ11−3i3i−3ζ73ζ7−3ζ113ζ110000000000000000000000000000000

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