Finite Group Databasebeta

← Group #11772590

Character table — Group #11772590

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1111222222222222224444444444444444444444448888888888888888888812121212121212121212121224242424242424242424242424242424242472727272
order124423346666121212121212222344466666666121212121212121212666666666612121212121212121212888824242424242424248888882424242424242424242424248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-111-1-1111-1-11111111111-1-11-1-1-111-1-1-1-11-1-1-111-1-1-1-1111111111111-1-1ii−i−i-1-1-1-1iiii−i−i−i−iii−i−i
χ61111111111111111111-1-111-1-1111-1-11111111111-1-11-1-1-111-1-1-1-11-1-1-111-1-1-1-1111111111111-1-1−i−iii-1-1-1-1−i−i−i−iiiii−i−iii
χ71111111111111111111-1-111-1-1111-1-11111111111-1-11-1-1-111-1-1-1-11-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i1111iiii−i−i−i−i−i−iii
χ81111111111111111111-1-111-1-1111-1-11111111111-1-11-1-1-111-1-1-1-11-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iii1111−i−i−i−iiiiiii−i−i
χ911-1-1111-11111-1-1-1-1-1-111-11-11-1111-1-1111-1-1-1-1-1-1-111111-11111-1-1-11-1-1-1-111-1-1ii−i−iiiii−i−i−i−ii−i1-11-1ii−i−i11-1-111-1-1i−ii−i
χ1011-1-1111-11111-1-1-1-1-1-111-11-11-1111-1-1111-1-1-1-1-1-1-111111-11111-1-1-11-1-1-1-111-1-1ii−i−iiiii−i−i−i−ii−i-11-11ii−i−i-1-111-1-111−ii−ii
χ1111-1-1111-11111-1-1-1-1-1-111-11-11-1111-1-1111-1-1-1-1-1-1-111111-11111-1-1-11-1-1-1-111-1-1−i−iii−i−i−i−iiiii−ii1-11-1−i−iii11-1-111-1-1−ii−ii
χ1211-1-1111-11111-1-1-1-1-1-111-11-11-1111-1-1111-1-1-1-1-1-1-111111-11111-1-1-11-1-1-1-111-1-1−i−iii−i−i−i−iiiii−ii-11-11−i−iii-1-111-1-111i−ii−i
χ1311-1-1111-11111-1-1-1-1-1-11-111-1-1111111111-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-111-1-1-1-111ii−i−iiiii−i−i−i−i−iii−i−ii−i−iiiii−i−i−i−iii-111-1
χ1411-1-1111-11111-1-1-1-1-1-11-111-1-1111111111-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-111-1-1-1-111ii−i−iiiii−i−i−i−i−ii−iii−i−i−iii−i−iiiii−i−i1-1-11
χ1511-1-1111-11111-1-1-1-1-1-11-111-1-1111111111-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-111-1-1-1-111−i−iii−i−i−i−iiiiii−ii−i−iiii−i−iii−i−i−i−iii1-1-11
χ1611-1-1111-11111-1-1-1-1-1-11-111-1-1111111111-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-111-1-1-1-111−i−iii−i−i−i−iiiiii−i−iii−iii−i−i−i−iiiii−i−i-111-1
χ17222222222222222222-22-22-2-222-2-2-2-22222-2-22222-2-2-222-2-2-222-2-2-2-222-2-2-2-2220000000000000000000000000000000000
χ18222222222222222222-2-222-22-22-2-2222222-2-2222222-2-2-22-2-2-2-222-22-2-2-2-222-2-20000000000000000000000000000000000
χ19222222-12222-1-1-12222222-1222-122-1-1-1-1-1-122-1-1-1-1-1-1-12-12-1-1-1-1-1-1-122-1-1-1-1-1-1-10000000000000022220000-1-1-1-1-1-1-1-10000
χ20222222-12222-1-1-12222222-1222-122-1-1-1-1-1-122-1-1-1-1-1-1-12-12-1-1-1-1-1-1-122-1-1-1-1-1-1-100000000000000-2-2-2-20000111111110000
χ21222222-12222-1-1-122222-2-2-12-2-2-12211-1-1-1-122-1-1-1-111-1-21-2-1-11111-1-2-21-1-11111000000000000002i2i−2i−2i0000−i−i−i−iiiii0000
χ22222222-12222-1-1-122222-2-2-12-2-2-12211-1-1-1-122-1-1-1-111-1-21-2-1-11111-1-2-21-1-1111100000000000000−2i−2i2i2i0000iiii−i−i−i−i0000
χ23222222-12222-1-1-12222-22-2-1-2-22-1-2-211-1-1-1-1-2-2-1-1-1-11112-1-211-1-1111-22-11111-1-100000000000000000000003−33−33−33−30000
χ24222222-12222-1-1-12222-22-2-1-2-22-1-2-211-1-1-1-1-2-2-1-1-1-11112-1-211-1-1111-22-11111-1-10000000000000000000000−33−33−33−330000
χ25222222-12222-1-1-12222-2-22-1-22-2-1-2-2-1-1-1-1-1-1-2-2-1-1-1-1-1-11-2121111-1-112-2111-1-1110000000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ26222222-12222-1-1-12222-2-22-1-22-2-1-2-2-1-1-1-1-1-1-2-2-1-1-1-1-1-11-2121111-1-112-2111-1-1110000000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ2722222-122-1-1-1222-1-1-1-1222-12222-1-122-1-1-12-1-1-1-1-1-1222-12-1-1-1-1-1-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1220000-1-1-1-1000000000000
χ2822222-122-1-1-1222-1-1-1-1222-12222-1-122-1-1-12-1-1-1-1-1-1222-12-1-1-1-1-1-1-12-1-12-1-1-1-1-1-1-2-2-2-211111111-2-200001111000000000000
χ2922222-122-1-1-1222-1-1-1-12-2-2-12-2-22-1-1-2-2-1-1-12-1-1-1-1-1-1-2-221-21-1-11111211-2-1-111112222-1-1-1-1-1-1-1-1-2-200001111000000000000
χ3022222-122-1-1-1222-1-1-1-12-2-2-12-2-22-1-1-2-2-1-1-12-1-1-1-1-1-1-2-221-21-1-11111211-2-1-11111-2-2-2-211111111220000-1-1-1-1000000000000
χ3122222-122-1-1-1222-1-1-1-1-22-2-1-2-22211-2-2-1-1-1211-1-1-1-1-2-2-2-12111-1-111-21-121111-1-10000−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i3000000000000
χ3222222-122-1-1-1222-1-1-1-1-22-2-1-2-22211-2-2-1-1-1211-1-1-1-1-2-2-2-12111-1-111-21-121111-1-10000i3i3−i3−i3i3i3−i3−i3000000i3−i3i3−i3000000000000
χ3322222-122-1-1-1222-1-1-1-1-2-22-1-22-221122-1-1-1211-1-1-1-122-21-2-11111-1-1-2-11-211-1-1110000−i3−i3i3i3−i3−i3i3i3000000i3−i3i3−i3000000000000
χ3422222-122-1-1-1222-1-1-1-1-2-22-1-22-221122-1-1-1211-1-1-1-122-21-2-11111-1-1-2-11-211-1-1110000i3i3−i3−i3i3i3−i3−i3000000−i3i3−i3i3000000000000
χ3522-2-2222-22222-2-2-2-2-2-2-22222-2-22-2-222222-222-2-2-2-2-2-2-2222-2-222222-2-2-222-2-2-2-20000000000000000000000000000000000
χ3622-2-2222-22222-2-2-2-2-2-2-2-2-222222-2-2-2-2222-222-2-2-2-222-2-2-2-2-2-2-2-2-2-222222222220000000000000000000000000000000000
χ3722-2-222-1-2222-111-2-2-2-222-2-1-22-2-12211-1-1-11-2-21111-1-1-12-1-2-1-1-1-11112-2111-1-111000000000000002-22-20000-1-111-1-1110000
χ3822-2-222-1-2222-111-2-2-2-222-2-1-22-2-12211-1-1-11-2-21111-1-1-12-1-2-1-1-1-11112-2111-1-11100000000000000-22-22000011-1-111-1-10000
χ3922-2-222-1-2222-111-2-2-2-22-22-1-2-22-122-1-1-1-1-11-2-2111111-1-212-1-111-1-11-22-11111-1-1000000000000002i−2i−2i2i0000−i−iiiii−i−i0000
χ4022-2-222-1-2222-111-2-2-2-22-22-1-2-22-122-1-1-1-1-11-2-2111111-1-212-1-111-1-11-22-11111-1-100000000000000−2i2i2i−2i0000ii−i−i−i−iii0000
χ4122-2-222-1-2222-111-2-2-2-2-222-12-2-2-1-2-2-1-1-1-1-112211111112-1211-1-1-1-1-1-2-21-1-1111100000000000000000000003−3−333−3−330000
χ4222-2-222-1-2222-111-2-2-2-2-222-12-2-2-1-2-2-1-1-1-1-112211111112-1211-1-1-1-1-1-2-21-1-111110000000000000000000000−333−3−333−30000
χ4322-2-222-1-2222-111-2-2-2-2-2-2-2-1222-1-2-211-1-1-11221111-1-11-21-2111111-122-1-1-1-1-1-1-10000000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ4422-2-222-1-2222-111-2-2-2-2-2-2-2-1222-1-2-211-1-1-11221111-1-11-21-2111111-122-1-1-1-1-1-1-10000000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ4522-2-22-12-2-1-1-12-2-2111122-2-1-22-22-1-1-2-2-1-1-1-2111111222-121-1-1-1-111-2-11-211-1-1112i2i−2i−2i−i−i−i−iiiii2i−2i0000−i−iii000000000000
χ4622-2-22-12-2-1-1-12-2-2111122-2-1-22-22-1-1-2-2-1-1-1-2111111222-121-1-1-1-111-2-11-211-1-111−2i−2i2i2iiiii−i−i−i−i−2i2i0000ii−i−i000000000000
χ4722-2-22-12-2-1-1-12-2-211112-22-1-2-222-1-122-1-1-1-2111111-2-221-2-1-1-111-1-1-21-121111-1-12i2i−2i−2i−i−i−i−iiiii−2i2i0000ii−i−i000000000000
χ4822-2-22-12-2-1-1-12-2-211112-22-1-2-222-1-122-1-1-1-2111111-2-221-2-1-1-111-1-1-21-121111-1-1−2i−2i2i2iiiii−i−i−i−i2i−2i0000−i−iii000000000000
χ4922-2-22-12-2-1-1-12-2-21111-222-12-2-221122-1-1-1-2-1-11111-2-2-2-12-111-1-1-1-1211-2-1-11111000033−3−3−3−3330000003−3−33000000000000
χ5022-2-22-12-2-1-1-12-2-21111-222-12-2-221122-1-1-1-2-1-11111-2-2-2-12-111-1-1-1-1211-2-1-111110000−3−33333−3−3000000−333−3000000000000
χ5122-2-22-12-2-1-1-12-2-21111-2-2-2-1222211-2-2-1-1-1-2-1-1111122-21-211111112-1-12-1-1-1-1-1-1000033−3−3−3−333000000−333−3000000000000
χ5222-2-22-12-2-1-1-12-2-21111-2-2-2-1222211-2-2-1-1-1-2-1-1111122-21-211111112-1-12-1-1-1-1-1-10000−3−33333−3−30000003−3−33000000000000
χ5344444-2-24-2-2-2-2-2-2-2-2-2-24441444-2-2-2-2-2111-2-2-21111-2-2-2-2-2-2111111-2-2-2-21111110000000000000000000000000000000000
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χ5544444-2-24-2-2-2-2-2-2-2-2-2-2-44-41-4-44-22222111-2221111222-2-22-1-111-1-122-2-2-1-1-1-1110000000000000000000000000000000000
χ5644444-2-24-2-2-2-2-2-2-2-2-2-2-4-441-44-4-222-2-2111-2221111-2-2222-2-1-1-1-1112-222-1-111-1-10000000000000000000000000000000000
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χ6944-4-44-2-2-4-2-2-2-2222222-4-4-41444-222221112-2-2-1-1-1-1-2-22222-1-1-1-1-1-1-2-2-2-21111110000000000000000000000000000000000
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χ874-4−4i4i0-240−2i32i32-4−4i4i2i−2i−2323000-200000000−2i32i320002i−2i−23230000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ13−2ζ132ζ5−2ζ5−2ζ72ζ7−2ζ232ζ230000000000000000000000
χ884-4−4i4i0-240−2i32i32-4−4i4i2i−2i−2323000-200000000−2i32i320002i−2i−232300000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ132ζ13−2ζ52ζ52ζ7−2ζ72ζ23−2ζ230000000000000000000000
χ894-4−4i4i0-2402i3−2i32-4−4i4i2i−2i23−23000-2000000002i3−2i320002i−2i23−230000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ5−2ζ52ζ13−2ζ13−2ζ232ζ23−2ζ72ζ70000000000000000000000
χ904-4−4i4i0-2402i3−2i32-4−4i4i2i−2i23−23000-2000000002i3−2i320002i−2i23−2300000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ52ζ5−2ζ132ζ132ζ23−2ζ232ζ7−2ζ70000000000000000000000
χ918-88i−8i08-4000-84−4i4i8i−8i00000-400000000004000−4i4i0000000000000000000000000000000000000000000000000000000000
χ928-88i−8i0-4-40−4i34i344−4i4i−4i4i43−430002000000002i3−2i3-20002i−2i−232300000000000000000000000000000000000000000000000000000000
χ938-88i−8i0-4-404i3−4i344−4i4i−4i4i−4343000200000000−2i32i3-20002i−2i23−2300000000000000000000000000000000000000000000000000000000
χ948-8−8i8i08-4000-844i−4i−8i8i00000-4000000000040004i−4i0000000000000000000000000000000000000000000000000000000000
χ958-8−8i8i0-4-40−4i34i3444i−4i4i−4i−43430002000000002i3−2i3-2000−2i2i23−2300000000000000000000000000000000000000000000000000000000
χ968-8−8i8i0-4-404i3−4i3444i−4i4i−4i43−43000200000000−2i32i3-2000−2i2i−232300000000000000000000000000000000000000000000000000000000

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