Finite Group Databasebeta

← Group #11786581

Character table — Group #11786581

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222222222444444444444444444888888888888888888888812121212121212121212121212121212121212122424242424242424242424242424363636367272
order12222233444466666666663666666666121212121212121244121212121212121212121212121212121212121222224444444412121212121212126666881212121224242424444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111111111-1-1
χ911-1-11-111-1-11111-111-1-1-1-1-111-111-1-1-11-1111-1-1-1-11i−iii−i−iii−i−i11-1-1iiii−i−i−i−i11-1-1i−ii−iii−i−iiiii−i−i−i−i11-1-11-1i−ii−i11-1-1i−ii−i1-1
χ1011-1-11-111-1-11111-111-1-1-1-1-111-111-1-1-11-1111-1-1-1-11i−iii−i−iii−i−i11-1-1iiii−i−i−i−i11-1-1−ii−iiii−i−iiiii−i−i−i−i11-1-1-11−ii−ii-1-111−ii−ii-11
χ1111-1-11-111-1-11111-111-1-1-1-1-111-111-1-1-11-1111-1-1-1-11i−iii−i−iii−i−i11-1-1iiii−i−i−i−i-1-111i−ii−i−i−iii−i−i−i−iiiii-1-1111-1i−ii−i11-1-1−ii−ii-11
χ1211-1-11-111-1-11111-111-1-1-1-1-111-111-1-1-11-1111-1-1-1-11i−iii−i−iii−i−i11-1-1iiii−i−i−i−i-1-111−ii−ii−i−iii−i−i−i−iiiii-1-111-11−ii−ii-1-111i−ii−i1-1
χ1311-1-11-111-1-11111-111-1-1-1-1-111-111-1-1-11-1111-1-1-1-11−ii−i−iii−i−iii11-1-1−i−i−i−iiiii11-1-1i−ii−i−i−iii−i−i−i−iiiii11-1-1-11i−ii−i-1-111i−ii−i-11
χ1411-1-11-111-1-11111-111-1-1-1-1-111-111-1-1-11-1111-1-1-1-11−ii−i−iii−i−iii11-1-1−i−i−i−iiiii11-1-1−ii−ii−i−iii−i−i−i−iiiii11-1-11-1−ii−ii11-1-1−ii−ii1-1
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χ1611-1-11-111-1-11111-111-1-1-1-1-111-111-1-1-11-1111-1-1-1-11−ii−i−iii−i−iii11-1-1−i−i−i−iiiii-1-111−ii−iiii−i−iiiii−i−i−i−i-1-1111-1−ii−ii11-1-1i−ii−i-11
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χ1822222222-2-2-2-222222222222222222222-2-2-2-2-2-2-2-20000000000-2-2-2-200000000-22-220000000000000000-22-220000000000000000
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χ202222222-12222-1-1-12-1-12-1-12-122-1-1-1-1-1-1-12-1-122-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-2-2-21111111111110000000000000000
χ212222222-12222-1-1-12-1-12-1-12-122-1-1-1-1-1-1-12-1-122-1-12-2-21111-2-2-2-2-1-1-1-11111111122220000-2-2-2-211111111-1-1-1-10000000000000000
χ222222222-12222-1-1-12-1-12-1-12-122-1-1-1-1-1-1-12-1-122-1-12-2-21111-2-2-2-2-1-1-1-111111111-2-2-2-200002222-1-1-1-1-1-1-1-111110000000000000000
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χ27222222-122222222-122-122-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100002222000000000000000022-1-1-1-1-1-1-1-1000000
χ28222222-122222222-122-122-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-20000000000000000-2-211111111000000
χ29222222-122222222-122-122-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-2-2-2-2-2-21111-1-1-1-111111111000022220000000000000000-2-2-1-1-1-11111000000
χ30222222-122222222-122-122-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-2-2-2-2-2-21111-1-1-1-1111111110000-2-2-2-20000000000000000221111-1-1-1-1000000
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χ4222-2-22-22-122-2-2-1-112-11-211-2-12-2-1-1111-11-21122-1-1-2003−3−33000011-1-133−3−3−3−333-222-200000000−3−33333−3−31-1-110000000000000000
χ4322-2-22-22-122-2-2-1-112-11-211-2-12-2-1-1111-11-21122-1-1-200−333−3000011-1-1−3−33333−3−32-2-2200000000−3−33333−3−3-111-10000000000000000
χ4422-2-22-22-122-2-2-1-112-11-211-2-12-2-1-1111-11-21122-1-1-200−333−3000011-1-1−3−33333−3−3-222-20000000033−3−3−3−3331-1-110000000000000000
χ4522-2-22-22-1-2-222-1-112-11-211-2-12-2-1-1111-112-1-1-2-21122i−2i−i−iii2i2i−2i−2i-1-111−i−i−i−iiiii22-2-200002i2i−2i−2i−i−i−i−iiiii-1-1110000000000000000
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χ5422-2-2-22222-2-22-2-2-222-2-222-22-22-2-2-2222-22-222-22-2-20000000000-222-2000000000000000000000000000000000000000000−2i2i2i−2i00
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χ924-4-440044000000-4-4-44-400440000-400-4400000000000000000000000000000000000000-222-2-22-222-22-200000000000000000000
χ934-4-44004-20000−2i32i32-42-2-42i3−2i34-200−2i32i322i3−2i32-2000000000000000000000000000000000000002-2-22−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i300000000000000000000
χ944-4-44004-20000−2i32i32-42-2-42i3−2i34-200−2i32i322i3−2i32-200000000000000000000000000000000000000-222-21−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i300000000000000000000
χ954-4-44004-200002i3−2i32-42-2-4−2i32i34-2002i3−2i32−2i32i32-2000000000000000000000000000000000000002-2-22−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i300000000000000000000
χ964-4-44004-200002i3−2i32-42-2-4−2i32i34-2002i3−2i32−2i32i32-200000000000000000000000000000000000000-222-21+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i300000000000000000000
χ978-88-800-4800000084-8-8-4004-40000-400440000000000000000000000000000000000000000000000000000000000000000000000
χ988-88-800-4-40000−4i34i3-4444-4−4i34i342002i3−2i322i3−2i3-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ998-88-800-4-400004i3−4i3-4444-44i3−4i34200−2i32i32−2i32i3-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-8800-48000000-84-88400-4-400004004-40000000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-8800-4-40000−4i34i3444-444i3−4i3-42002i3−2i3-2−2i32i3-220000000000000000000000000000000000000000000000000000000000000000000000
χ1028-8-8800-4-400004i3−4i3444-44−4i34i3-4200−2i32i3-22i3−2i3-220000000000000000000000000000000000000000000000000000000000000000000000

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