Finite Group Databasebeta

← Group #11771429

Character table — Group #11771429

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1111222222222222224444444444444444444444448888888888888888888812121212121212121212121224242424242424242424242424242424242472727272
order124423346666121212121212234666666888812121212121212242424246661212122424242424242424242424242424888824242424242424242466121216161616484848484848484816161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
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
χ5111111111111111111111111111-1-1-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1ii−i−iiiii−i−i−i−iii−i−i
χ6111111111111111111111111111-1-1-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1−i−iii−i−i−i−iiiii−i−iii
χ7111111111111111111111111111-1-1-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111ii−i−iiiii−i−i−i−i−i−iii
χ8111111111111111111111111111-1-1-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−iii−i−i−i−iiiiiii−i−i
χ911-1-1111-11111-1-1-1-1-1-1-1111-1-1111i−ii−i-111-1-1-1-1ii−i−i-1-1-1111iii−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−i1-111-1-1ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ1011-1-1111-11111-1-1-1-1-1-1-1111-1-1111i−ii−i-111-1-1-1-1ii−i−i-1-1-1111iii−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−i1-111-1-1−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ1111-1-1111-11111-1-1-1-1-1-1-1111-1-1111i−ii−i-111-1-1-1-1ii−i−i-1-1-1111iii−i−i−iiiii−i−i−i−i−i−iii−i−i−i−iiiii-11-1-111ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ1211-1-1111-11111-1-1-1-1-1-1-1111-1-1111i−ii−i-111-1-1-1-1ii−i−i-1-1-1111iii−i−i−iiiii−i−i−i−i−i−iii−i−i−i−iiiii-11-1-111−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ1311-1-1111-11111-1-1-1-1-1-1-1111-1-1111−ii−ii-111-1-1-1-1−i−iii-1-1-1111−i−i−iiii−i−i−i−iiiiiii−i−iiiii−i−i−i−i-11-1-111−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ1411-1-1111-11111-1-1-1-1-1-1-1111-1-1111−ii−ii-111-1-1-1-1−i−iii-1-1-1111−i−i−iiii−i−i−i−iiiiiii−i−iiiii−i−i−i−i-11-1-111ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ1511-1-1111-11111-1-1-1-1-1-1-1111-1-1111−ii−ii-111-1-1-1-1−i−iii-1-1-1111−i−i−iiii−i−i−i−iiiii−i−iii−i−i−i−iiiii1-111-1-1−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ1611-1-1111-11111-1-1-1-1-1-1-1111-1-1111−ii−ii-111-1-1-1-1−i−iii-1-1-1111−i−i−iiii−i−i−i−iiiii−i−iii−i−i−i−iiiii1-111-1-1ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
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χ20222222-12-1-12-122-1-1-1-12-122-1-1-1-1-122222-1-1-1-1-1-122222-1-12-1-1-12-1-12-1-1-1-1-1-1-1-1-1-2-2-2-211111111-2-211110000000000000000
χ21222222-12-1-12-122-1-1-1-12-122-1-1-1-1-1-2-2-2-22-1-1-1-1-1-1-2-2-2-22-1-12-1-11-211-21111111112222-1-1-1-1-1-1-1-1-2-211110000000000000000
χ22222222-12-1-12-122-1-1-1-12-122-1-1-1-1-1-2-2-2-22-1-1-1-1-1-1-2-2-2-22-1-12-1-11-211-2111111111-2-2-2-21111111122-1-1-1-10000000000000000
χ23222222-12-1-12-122-1-1-1-1-2-1-2211-1-1-122-2-2211-1-1-1-12222-211-211-1-21-1-21-1-111-1-1110000−i3−i3i3i3−i3−i3i3i300−i3i3−i3i30000000000000000
χ24222222-12-1-12-122-1-1-1-1-2-1-2211-1-1-122-2-2211-1-1-1-12222-211-211-1-21-1-21-1-111-1-1110000i3i3−i3−i3i3i3−i3−i300i3−i3i3−i30000000000000000
χ25222222-12-1-12-122-1-1-1-1-2-1-2211-1-1-1-2-222211-1-1-1-1-2-2-2-2-211-21112-112-111-1-111-1-10000−i3−i3i3i3−i3−i3i3i300i3−i3i3−i30000000000000000
χ26222222-12-1-12-122-1-1-1-1-2-1-2211-1-1-1-2-222211-1-1-1-1-2-2-2-2-211-21112-112-111-1-111-1-10000i3i3−i3−i3i3i3−i3−i300−i3i3−i3i30000000000000000
χ2722222-12222-12-1-122222-12-122-1-1-12222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-12-122-12-1-1-1-1-1-1-1-10000000000000000002222-1-1-1-1-1-1-1-10000
χ2822222-12222-12-1-122222-12-122-1-1-12222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-12-122-12-1-1-1-1-1-1-1-1000000000000000000-2-2-2-2111111110000
χ2922222-12222-12-1-122222-12-122-1-1-1-2-2-2-2-122-1-1-1-11111-1-1-1-1-1-1-21-2-21-2111111110000000000000000002i2i−2i−2i−i−i−i−iiiii0000
χ3022222-12222-12-1-122222-12-122-1-1-1-2-2-2-2-122-1-1-1-11111-1-1-1-1-1-1-21-2-21-211111111000000000000000000−2i−2i2i2iiiii−i−i−i−i0000
χ3122222-12222-12-1-12222-2-1-2-1-2-2-1-1-122-2-2-1-2-2-1-1-1-1-1-1-1-111111121-221-2-1-111-1-1110000000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ3222222-12222-12-1-12222-2-1-2-1-2-2-1-1-122-2-2-1-2-2-1-1-1-1-1-1-1-111111121-221-2-1-111-1-1110000000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ3322222-12222-12-1-12222-2-1-2-1-2-2-1-1-1-2-222-1-2-2-1-1-1-11111111111-2-12-2-1211-1-111-1-100000000000000000000003−33−3−33−330000
χ3422222-12222-12-1-12222-2-1-2-1-2-2-1-1-1-2-222-1-2-2-1-1-1-11111111111-2-12-2-1211-1-111-1-10000000000000000000000−33−333−33−30000
χ3522-2-2222-22222-2-2-2-2-2-222-22222222i−2i−2i2i-2-2-2-2-2-2-22i2i−2i−2i222-2-2-22i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000
χ3622-2-2222-22222-2-2-2-2-2-222-2222222−2i2i2i−2i-2-2-2-2-2-2-2−2i−2i2i2i222-2-2-2−2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000
χ3722-2-222-1-2-1-12-1-2-211112-1-22-1-1-1-1-12i−2i−2i2i-21111112i2i−2i−2i2-1-1-211−i−2iii2i−i−i−iiiii−i−i000033−3−3−3−33300−i3i3i3−i30000000000000000
χ3822-2-222-1-2-1-12-1-2-211112-1-22-1-1-1-1-12i−2i−2i2i-21111112i2i−2i−2i2-1-1-211−i−2iii2i−i−i−iiiii−i−i0000−3−33333−3−300i3−i3−i3i30000000000000000
χ3922-2-222-1-2-1-12-1-2-211112-1-22-1-1-1-1-1−2i2i2i−2i-2111111−2i−2i2i2i2-1-1-211i2i−i−i−2iiii−i−i−i−iii000033−3−3−3−33300i3−i3−i3i30000000000000000
χ4022-2-222-1-2-1-12-1-2-211112-1-22-1-1-1-1-1−2i2i2i−2i-2111111−2i−2i2i2i2-1-1-211i2i−i−i−2iiii−i−i−i−iii0000−3−33333−3−300−i3i3i3−i30000000000000000
χ4122-2-222-1-2-1-12-1-2-21111-2-12211-1-1-12i−2i2i−2i-2-1-111112i2i−2i−2i-2112-1-1−i2i−ii−2ii−i−i−i−iiiii2i2i−2i−2i−i−i−i−iiiii2-2-1-1110000000000000000
χ4222-2-222-1-2-1-12-1-2-21111-2-12211-1-1-12i−2i2i−2i-2-1-111112i2i−2i−2i-2112-1-1−i2i−ii−2ii−i−i−i−iiiii−2i−2i2i2iiiii−i−i−i−i-2211-1-10000000000000000
χ4322-2-222-1-2-1-12-1-2-21111-2-12211-1-1-1−2i2i−2i2i-2-1-11111−2i−2i2i2i-2112-1-1i−2ii−i2i−iiiii−i−i−i−i2i2i−2i−2i−i−i−i−iiiii-2211-1-10000000000000000
χ4422-2-222-1-2-1-12-1-2-21111-2-12211-1-1-1−2i2i−2i2i-2-1-11111−2i−2i2i2i-2112-1-1i−2ii−i2i−iiiii−i−i−i−i−2i−2i2i2iiiii−i−i−i−i2-2-1-1110000000000000000
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χ4622-2-22-12-222-1211-2-2-2-22-1-2-122-1-1-12i−2i−2i2i1-2-21111−i−iii-1-1-11112ii−2i−2i−i2i−i−iiiii−i−i0000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000
χ4722-2-22-12-222-1211-2-2-2-22-1-2-122-1-1-1−2i2i2i−2i1-2-21111ii−i−i-1-1-1111−2i−i2i2ii−2iii−i−i−i−iii0000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ230000
χ4822-2-22-12-222-1211-2-2-2-22-1-2-122-1-1-1−2i2i2i−2i1-2-21111ii−i−i-1-1-1111−2i−i2i2ii−2iii−i−i−i−iii0000000000000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ230000
χ4922-2-22-12-222-1211-2-2-2-2-2-12-1-2-2-1-1-12i−2i2i−2i1221111−i−iii111-1-1-12i−i2i−2ii−2i−i−i−i−iiiii0000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ130000
χ5022-2-22-12-222-1211-2-2-2-2-2-12-1-2-2-1-1-12i−2i2i−2i1221111−i−iii111-1-1-12i−i2i−2ii−2i−i−i−i−iiiii000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ130000
χ5122-2-22-12-222-1211-2-2-2-2-2-12-1-2-2-1-1-1−2i2i−2i2i1221111ii−i−i111-1-1-1−2ii−2i2i−i2iiiii−i−i−i−i000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ230000
χ5222-2-22-12-222-1211-2-2-2-2-2-12-1-2-2-1-1-1−2i2i−2i2i1221111ii−i−i111-1-1-1−2ii−2i2i−i2iiiii−i−i−i−i0000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ230000
χ5344444-2-24-2-2-2-2-2-2-2-2-2-2414-2-2-21114444-2-2-21111-2-2-2-2-211-211-2-2-2-2-2-2111111110000000000000000000000000000000000
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χ7744-4-4-4-2-2422-2-22222-2-201022i3−2i3-1-110000-2−2i32i311-1-123−23−23230−i3i30i3−i3000000−333i−3i3−3−3i3i0000000000000000000000000000000000
χ7844-4-4-4-2-2422-2-22222-2-201022i3−2i3-1-110000-2−2i32i311-1-1−232323−230−i3i30i3−i30000003−3−3i3i−333i−3i0000000000000000000000000000000000
χ794-44i−4i044000-4-44i−4i4i−4i0004000000-40000000004i−4i0000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000000000
χ804-44i−4i044000-4-44i−4i4i−4i0004000000-40000000004i−4i000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000000000
χ814-44i−4i04-20−2i32i3-424i−4i−2i2i23−230-20000−2i32i32000000023−23−2i2i0000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ72ζ7−2ζ232ζ232ζ13−2ζ132ζ5−2ζ50000000000000000000000
χ824-44i−4i04-20−2i32i3-424i−4i−2i2i23−230-20000−2i32i32000000023−23−2i2i000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7−2ζ72ζ23−2ζ23−2ζ132ζ13−2ζ52ζ50000000000000000000000
χ834-44i−4i04-202i3−2i3-424i−4i−2i2i−23230-200002i3−2i320000000−2323−2i2i0000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ232ζ23−2ζ72ζ72ζ5−2ζ52ζ13−2ζ130000000000000000000000
χ844-44i−4i04-202i3−2i3-424i−4i−2i2i−23230-200002i3−2i320000000−2323−2i2i000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ23−2ζ232ζ7−2ζ7−2ζ52ζ5−2ζ132ζ130000000000000000000000
χ854-4−4i4i044000-4-4−4i4i−4i4i0004000000-4000000000−4i4i000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000000000
χ864-4−4i4i044000-4-4−4i4i−4i4i0004000000-4000000000−4i4i0000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000000000
χ874-4−4i4i04-20−2i32i3-42−4i4i2i−2i−23230-20000−2i32i320000000−23232i−2i000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ13−2ζ132ζ5−2ζ5−2ζ72ζ7−2ζ232ζ230000000000000000000000
χ884-4−4i4i04-20−2i32i3-42−4i4i2i−2i−23230-20000−2i32i320000000−23232i−2i0000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ132ζ13−2ζ52ζ52ζ7−2ζ72ζ23−2ζ230000000000000000000000
χ894-4−4i4i04-202i3−2i3-42−4i4i2i−2i23−230-200002i3−2i32000000023−232i−2i000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ5−2ζ52ζ13−2ζ13−2ζ232ζ23−2ζ72ζ70000000000000000000000
χ904-4−4i4i04-202i3−2i3-42−4i4i2i−2i23−230-200002i3−2i32000000023−232i−2i0000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ52ζ5−2ζ132ζ132ζ23−2ζ232ζ7−2ζ70000000000000000000000
χ918-88i−8i0-480004-8−4i4i8i−8i000-40000004000000000−4i4i0000000000000000000000000000000000000000000000000000000000
χ928-88i−8i0-4-40−4i34i344−4i4i−4i4i43−430200002i3−2i3-20000000−23232i−2i0000000000000000000000000000000000000000000000000000000000
χ938-88i−8i0-4-404i3−4i344−4i4i−4i4i−4343020000−2i32i3-2000000023−232i−2i0000000000000000000000000000000000000000000000000000000000
χ948-8−8i8i0-480004-84i−4i−8i8i000-400000040000000004i−4i0000000000000000000000000000000000000000000000000000000000
χ958-8−8i8i0-4-40−4i34i3444i−4i4i−4i−43430200002i3−2i3-2000000023−23−2i2i0000000000000000000000000000000000000000000000000000000000
χ968-8−8i8i0-4-404i3−4i3444i−4i4i−4i43−43020000−2i32i3-20000000−2323−2i2i0000000000000000000000000000000000000000000000000000000000

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