Finite Group Databasebeta

← Group #11771508

Character table — Group #11771508

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1111222222222222224444444444444444444444448888888888888888888812121212121212121212121224242424242424242424242424242424242472727272
order12442334666612121212121223466666688881212121212121224242424666121212242424242424242424242424242444441212121212121212881616161624242424484848484848484816161616
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
χ5111111111111111111111111111-1-1-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1ii−i−i-1-1-1-1iiii−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−i−iii-1-1-1-1−i−i−i−iiiii−i−iii
χ7111111111111111111111111111-1-1-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i1111iiii−i−i−i−i−i−iii
χ8111111111111111111111111111-1-1-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iii1111−i−i−i−iiiiiii−i−i
χ911-1-1111-11111-1-1-1-1-1-1-1111-1-1111i−ii−i11-1-1-1-1-1ii−i−i-1-1-1111i−iii−i−iiiii−i−i−i−i11-1-11111-1-1-1-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ii−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ1011-1-1111-11111-1-1-1-1-1-1-1111-1-1111i−ii−i11-1-1-1-1-1ii−i−i-1-1-1111i−iii−i−iiiii−i−i−i−i11-1-11111-1-1-1-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ii−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ1111-1-1111-11111-1-1-1-1-1-1-1111-1-1111i−ii−i11-1-1-1-1-1ii−i−i-1-1-1111i−iii−i−iiiii−i−i−i−i-1-111-1-1-1-11111−iiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−i−iiiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ1211-1-1111-11111-1-1-1-1-1-1-1111-1-1111i−ii−i11-1-1-1-1-1ii−i−i-1-1-1111i−iii−i−iiiii−i−i−i−i-1-111-1-1-1-11111−ii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−i−iii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ1311-1-1111-11111-1-1-1-1-1-1-1111-1-1111−ii−ii11-1-1-1-1-1−i−iii-1-1-1111−ii−i−iii−i−i−i−iiiii11-1-11111-1-1-1-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−i−iii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ1411-1-1111-11111-1-1-1-1-1-1-1111-1-1111−ii−ii11-1-1-1-1-1−i−iii-1-1-1111−ii−i−iii−i−i−i−iiiii11-1-11111-1-1-1-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−i−iiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ1511-1-1111-11111-1-1-1-1-1-1-1111-1-1111−ii−ii11-1-1-1-1-1−i−iii-1-1-1111−ii−i−iii−i−i−i−iiiii-1-111-1-1-1-11111i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ii−i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ1611-1-1111-11111-1-1-1-1-1-1-1111-1-1111−ii−ii11-1-1-1-1-1−i−iii-1-1-1111−ii−i−iii−i−i−i−iiiii-1-111-1-1-1-11111i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ii−i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ17222222222222222222-22-22-2-222222-2-2-2-2222222222-2-2-2-2-2-2-2-22-22-222-2-222-2-20000000000000000000000000000000000
χ18222222222222222222-22-22-2-2222-2-222-2-222222-2-2-2-2-2-2-2-2-2-222-22-22-2-222-2-2220000000000000000000000000000000000
χ19222222-122-12222-1-1222-12-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000022220000-1-1-1-1-1-1-1-10000
χ20222222-122-12222-1-1222-12-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000-2-2-2-20000111111110000
χ21222222-122-12222-1-1222-12-122-1-1-1-2-2-2-222-1-1-1-1-11111-1-1-1-1-1-111-2-2-2-211111111000000000000002i2i−2i−2i0000−i−i−i−iiiii0000
χ22222222-122-12222-1-1222-12-122-1-1-1-2-2-2-222-1-1-1-1-11111-1-1-1-1-1-111-2-2-2-21111111100000000000000−2i−2i2i2i0000iiii−i−i−i−i0000
χ23222222-122-12222-1-122-2-1-2-1-2-2-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1111111112-22-2-1-111-1-1110000000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ24222222-122-12222-1-122-2-1-2-1-2-2-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1111111112-22-2-1-111-1-1110000000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ25222222-122-12222-1-122-2-1-2-1-2-2-1-1-1-2-222-2-2-1-1-1-1-11111111111-1-1-22-2211-1-111-1-100000000000000000000003−33−3−33−330000
χ26222222-122-12222-1-122-2-1-2-1-2-2-1-1-1-2-222-2-2-1-1-1-1-11111111111-1-1-22-2211-1-111-1-10000000000000000000000−33−333−33−30000
χ2722222-122-12-1-1-1-122-1-12-122-1-1-1-1-12222-1-12-1-1-1-122222-1-12-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1220000-1-1-1-1000000000000
χ2822222-122-12-1-1-1-122-1-12-122-1-1-1-1-12222-1-12-1-1-1-122222-1-12-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111-2-200001111000000000000
χ2922222-122-12-1-1-1-122-1-12-122-1-1-1-1-1-2-2-2-2-1-12-1-1-1-1-2-2-2-22-1-12-1-1-2-21111111111112222-1-1-1-1-1-1-1-1-2-200001111000000000000
χ3022222-122-12-1-1-1-122-1-12-122-1-1-1-1-1-2-2-2-2-1-12-1-1-1-1-2-2-2-22-1-12-1-1-2-2111111111111-2-2-2-211111111220000-1-1-1-1000000000000
χ3122222-122-12-1-1-1-122-1-1-2-1-2211-1-1-122-2-2112-1-1-1-12222-211-211-2-2-11-11-1-111-1-1110000−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i3000000000000
χ3222222-122-12-1-1-1-122-1-1-2-1-2211-1-1-122-2-2112-1-1-1-12222-211-211-2-2-11-11-1-111-1-1110000i3i3−i3−i3i3i3−i3−i3000000i3−i3i3−i3000000000000
χ3322222-122-12-1-1-1-122-1-1-2-1-2211-1-1-1-2-222112-1-1-1-1-2-2-2-2-211-211221-11-111-1-111-1-10000−i3−i3i3i3−i3−i3i3i3000000i3−i3i3−i3000000000000
χ3422222-122-12-1-1-1-122-1-1-2-1-2211-1-1-1-2-222112-1-1-1-1-2-2-2-2-211-211221-11-111-1-111-1-10000i3i3−i3−i3i3i3−i3−i3000000−i3i3−i3i3000000000000
χ3522-2-2222-22222-2-2-2-2-2-222-22222222i−2i−2i2i-2-2-2-2-2-2-22i2i−2i−2i222-2-2-2−2i2i2i−2i−2i2i2i2i−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−2i2i2i222-2-2-22i−2i−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000
χ3722-2-222-1-22-122-2-211-2-22-1-2-122-1-1-12i−2i−2i2i-2-211111−i−iii-1-1-1111i−i2i−2i−2i2i−i−iiiii−i−i0000000000000000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ130000
χ3822-2-222-1-22-122-2-211-2-22-1-2-122-1-1-12i−2i−2i2i-2-211111−i−iii-1-1-1111i−i2i−2i−2i2i−i−iiiii−i−i0000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000
χ3922-2-222-1-22-122-2-211-2-22-1-2-122-1-1-1−2i2i2i−2i-2-211111ii−i−i-1-1-1111−ii−2i2i2i−2iii−i−i−i−iii0000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ230000
χ4022-2-222-1-22-122-2-211-2-22-1-2-122-1-1-1−2i2i2i−2i-2-211111ii−i−i-1-1-1111−ii−2i2i2i−2iii−i−i−i−iii0000000000000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ230000
χ4122-2-222-1-22-122-2-211-2-2-2-12-1-2-2-1-1-12i−2i2i−2i2211111−i−iii111-1-1-1−ii2i2i−2i−2i−i−i−i−iiiii000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ130000
χ4222-2-222-1-22-122-2-211-2-2-2-12-1-2-2-1-1-12i−2i2i−2i2211111−i−iii111-1-1-1−ii2i2i−2i−2i−i−i−i−iiiii00000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ130000
χ4322-2-222-1-22-122-2-211-2-2-2-12-1-2-2-1-1-1−2i2i−2i2i2211111ii−i−i111-1-1-1i−i−2i−2i2i2iiiii−i−i−i−i00000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ230000
χ4422-2-222-1-22-122-2-211-2-2-2-12-1-2-2-1-1-1−2i2i−2i2i2211111ii−i−i111-1-1-1i−i−2i−2i2i2iiiii−i−i−i−i000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ230000
χ4522-2-22-12-2-12-1-111-2-2112-1-22-1-1-1-1-12i−2i−2i2i11-211112i2i−2i−2i2-1-1-211−2i2i−iii−i−i−iiiii−i−i0000−i3−i3i3i3i3i3−i3−i30000003−3−33000000000000
χ4622-2-22-12-2-12-1-111-2-2112-1-22-1-1-1-1-12i−2i−2i2i11-211112i2i−2i−2i2-1-1-211−2i2i−iii−i−i−iiiii−i−i0000i3i3−i3−i3−i3−i3i3i3000000−333−3000000000000
χ4722-2-22-12-2-12-1-111-2-2112-1-22-1-1-1-1-1−2i2i2i−2i11-21111−2i−2i2i2i2-1-1-2112i−2ii−i−iiii−i−i−i−iii0000−i3−i3i3i3i3i3−i3−i3000000−333−3000000000000
χ4822-2-22-12-2-12-1-111-2-2112-1-22-1-1-1-1-1−2i2i2i−2i11-21111−2i−2i2i2i2-1-1-2112i−2ii−i−iiii−i−i−i−iii0000i3i3−i3−i3−i3−i3i3i30000003−3−33000000000000
χ4922-2-22-12-2-12-1-111-2-211-2-12211-1-1-12i−2i2i−2i-1-1-211112i2i−2i−2i-2112-1-12i−2i−i−iii−i−i−i−iiiii22-2-2-1-1-1-111112i−2i0000−i−iii000000000000
χ5022-2-22-12-2-12-1-111-2-211-2-12211-1-1-12i−2i2i−2i-1-1-211112i2i−2i−2i-2112-1-12i−2i−i−iii−i−i−i−iiiii-2-2221111-1-1-1-1−2i2i0000ii−i−i000000000000
χ5122-2-22-12-2-12-1-111-2-211-2-12211-1-1-1−2i2i−2i2i-1-1-21111−2i−2i2i2i-2112-1-1−2i2iii−i−iiiii−i−i−i−i22-2-2-1-1-1-11111−2i2i0000ii−i−i000000000000
χ5222-2-22-12-2-12-1-111-2-211-2-12211-1-1-1−2i2i−2i2i-1-1-21111−2i−2i2i2i-2112-1-1−2i2iii−i−iiiii−i−i−i−i-2-2221111-1-1-1-12i−2i0000−i−iii000000000000
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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χ5644444-2-24-2-2-2-2-2-2-2-2-2-2-41-4-222111-4-44422-2111122222-1-12-1-1-2-22-22-2-1-111-1-1110000000000000000000000000000000000
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χ6844-4-44-2-2-4-2-2-2-2222222-414-2221114i−4i4i−4i-2-22-1-1-1-1−2i−2i2i2i2-1-1-211−2i2i−2i−2i2i2iiiii−i−i−i−i0000000000000000000000000000000000
χ6944-4-44-2-2-4-2-2-2-2222222-414-222111−4i4i−4i4i-2-22-1-1-1-12i2i−2i−2i2-1-1-2112i−2i2i2i−2i−2i−i−i−i−iiiii0000000000000000000000000000000000
χ7044-4-4-444444-4-444-4-4-4-4040-400-4-44000000444-4-40000000000000000000000000000000000000000000000000000000000
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χ7244-4-4-44-244-2-4-44422-4-40-2020022-2000000-2-2-222−232323−23000000000000−23230023−23000000000000000000000000000000000000
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χ7644-4-4-4-2-24-2-222-2-222220102−2i32i3-1-1100002i3−2i3-211-1-1−232323−230i3−i30−i3i30000003−33i−3i−33−3i3i0000000000000000000000000000000000
χ7744-4-4-4-2-24-2-222-2-2222201022i3−2i3-1-110000−2i32i3-211-1-123−23−23230−i3i30i3−i3000000−333i−3i3−3−3i3i0000000000000000000000000000000000
χ7844-4-4-4-2-24-2-222-2-2222201022i3−2i3-1-110000−2i32i3-211-1-1−232323−230−i3i30i3−i30000003−3−3i3i−333i−3i0000000000000000000000000000000000
χ794-44i−4i0440-4-400004i−4i4i−4i04000000-40000000004i−4i0000000000000000000000002-22i−2i2-22-22i−2i2i−2i0000000000000000000000
χ804-44i−4i0440-4-400004i−4i4i−4i04000000-40000000004i−4i000000000000000000000000-22−2i2i-22-22−2i2i−2i2i0000000000000000000000
χ814-44i−4i0-2402-4−2i32i323−234i−4i−2i2i0-20000−2i32i32000000023−23−2i2i0000000000000000000000002-22i−2i−1−i31+i3−1+i31−i32ζ22−2ζ222ζ14−2ζ140000000000000000000000
χ824-44i−4i0-2402-4−2i32i323−234i−4i−2i2i0-20000−2i32i32000000023−23−2i2i000000000000000000000000-22−2i2i1+i3−1−i31−i3−1+i3−2ζ222ζ22−2ζ142ζ140000000000000000000000
χ834-44i−4i0-2402-42i3−2i3−23234i−4i−2i2i0-200002i3−2i320000000−2323−2i2i0000000000000000000000002-22i−2i−1+i31−i3−1−i31+i32ζ14−2ζ142ζ22−2ζ220000000000000000000000
χ844-44i−4i0-2402-42i3−2i3−23234i−4i−2i2i0-200002i3−2i320000000−2323−2i2i000000000000000000000000-22−2i2i1−i3−1+i31+i3−1−i3−2ζ142ζ14−2ζ222ζ220000000000000000000000
χ854-4−4i4i0440-4-40000−4i4i−4i4i04000000-4000000000−4i4i0000000000000000000000002-2−2i2i2-22-2−2i2i−2i2i0000000000000000000000
χ864-4−4i4i0440-4-40000−4i4i−4i4i04000000-4000000000−4i4i000000000000000000000000-222i−2i-22-222i−2i2i−2i0000000000000000000000
χ874-4−4i4i0-2402-4−2i32i3−2323−4i4i2i−2i0-20000−2i32i320000000−23232i−2i0000000000000000000000002-2−2i2i−1−i31+i3−1+i31−i3−2ζ222ζ22−2ζ142ζ140000000000000000000000
χ884-4−4i4i0-2402-4−2i32i3−2323−4i4i2i−2i0-20000−2i32i320000000−23232i−2i000000000000000000000000-222i−2i1+i3−1−i31−i3−1+i32ζ22−2ζ222ζ14−2ζ140000000000000000000000
χ894-4−4i4i0-2402-42i3−2i323−23−4i4i2i−2i0-200002i3−2i32000000023−232i−2i0000000000000000000000002-2−2i2i−1+i31−i3−1−i31+i3−2ζ142ζ14−2ζ222ζ220000000000000000000000
χ904-4−4i4i0-2402-42i3−2i323−23−4i4i2i−2i0-200002i3−2i32000000023−232i−2i000000000000000000000000-222i−2i1−i3−1+i31+i3−1−i32ζ14−2ζ142ζ22−2ζ220000000000000000000000
χ918-88i−8i08-40-840000−4i4i8i−8i0-40000004000000000−4i4i0000000000000000000000000000000000000000000000000000000000
χ928-88i−8i0-4-4044−4i34i343−43−4i4i−4i4i0200002i3−2i3-20000000−23232i−2i0000000000000000000000000000000000000000000000000000000000
χ938-88i−8i0-4-40444i3−4i3−4343−4i4i−4i4i020000−2i32i3-2000000023−232i−2i0000000000000000000000000000000000000000000000000000000000
χ948-8−8i8i08-40-8400004i−4i−8i8i0-400000040000000004i−4i0000000000000000000000000000000000000000000000000000000000
χ958-8−8i8i0-4-4044−4i34i3−43434i−4i4i−4i0200002i3−2i3-2000000023−23−2i2i0000000000000000000000000000000000000000000000000000000000
χ968-8−8i8i0-4-40444i3−4i343−434i−4i4i−4i020000−2i32i3-20000000−2323−2i2i0000000000000000000000000000000000000000000000000000000000

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