Finite Group Databasebeta

← Group #10705313

Character table — Group #10705313

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222222222224444444444444444444466666666888888888812121212121212121212121216161616161616161616161648484848
order122234444446668888881212121212121616161616161616242424244444888824244848484848484848248816161616161616162466881212242424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111-1-1
χ911111-1-111-1-1111-1-1-1-111-1-111-1-1iiii−i−i−i−i-1-1-1-11111-1-1-1-111iiii−i−i−i−i-1-111iiii−i−i−i−i1-111i−i-1-1ii−i−i1-1i−i
χ1011111-1-111-1-1111-1-1-1-111-1-111-1-1iiii−i−i−i−i-1-1-1-11111-1-1-1-111iiii−i−i−i−i-1-111iiii−i−i−i−i-11-1-1−ii11−i−iii-11−ii
χ1111111-1-111-1-1111-1-1-1-111-1-111-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-1111111iiii−i−i−i−i11-1-1−i−i−i−iiiii1-111i−i-1-1ii−i−i-11−ii
χ1211111-1-111-1-1111-1-1-1-111-1-111-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-1111111iiii−i−i−i−i11-1-1−i−i−i−iiiii-11-1-1−ii11−i−iii1-1i−i
χ1311111-1-111-1-1111-1-1-1-111-1-111-1-1−i−i−i−iiiii-1-1-1-11111-1-1-1-111−i−i−i−iiiii-1-111−i−i−i−iiiii1-111−ii-1-1−i−iii1-1−ii
χ1411111-1-111-1-1111-1-1-1-111-1-111-1-1−i−i−i−iiiii-1-1-1-11111-1-1-1-111−i−i−i−iiiii-1-111−i−i−i−iiiii-11-1-1i−i11ii−i−i-11i−i
χ1511111-1-111-1-1111-1-1-1-111-1-111-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-1111111−i−i−i−iiiii11-1-1iiii−i−i−i−i1-111−ii-1-1−i−iii-11i−i
χ1611111-1-111-1-1111-1-1-1-111-1-111-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-1111111−i−i−i−iiiii11-1-1iiii−i−i−i−i-11-1-1i−i11ii−i−i1-1−ii
χ1722222222222222-2-2-2-2-2-222222200000000-2-2-2-22222-2-2-2-2-2-20000000022-2-2000000000000000000000000
χ1822222222222222-2-2-2-2-2-222222200000000-2-2-2-2-2-2-2-22222-2-200000000-2-222000000000000000000000000
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χ202222222-2-2-2-222200000022-2-2-2-2−i2−i2i2i2−i2−i2i2i20000-2-222000000−i2−i2i2i2−i2−i2i2i22-200i2i2−i2−i2i2i2−i2−i20000000000000000
χ212222222-2-2-2-222200000022-2-2-2-2i2i2−i2−i2i2i2−i2−i2000022-2-2000000i2i2−i2−i2i2i2−i2−i2-2200i2i2−i2−i2i2i2−i2−i20000000000000000
χ222222222-2-2-2-222200000022-2-2-2-2i2i2−i2−i2i2i2−i2−i20000-2-222000000i2i2−i2−i2i2i2−i2−i22-200−i2−i2i2i2−i2−i2i2i20000000000000000
χ2322222-2-222-2-22222222-2-2-2-222-2-200000000222222222222-2-200000000-2-2-2-2000000000000000000000000
χ2422222-2-222-2-22222222-2-2-2-222-2-2000000002222-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000
χ2522222-2-2-2-222222000000-2-2-2-22222−2−2−2−222000022-2-200000022−2−2−2−2222-20022−2−2−2−2220000000000000000
χ2622222-2-2-2-222222000000-2-2-2-22222−2−2−2−2220000-2-22200000022−2−2−2−222-2200−2−22222−2−20000000000000000
χ2722222-2-2-2-222222000000-2-2-2-222−2−22222−2−2000022-2-2000000−2−22222−2−22-200−2−22222−2−20000000000000000
χ2822222-2-2-2-222222000000-2-2-2-222−2−22222−2−20000-2-222000000−2−22222−2−2-220022−2−2−2−2220000000000000000
χ292222-1222222-1-1-1222222-1-1-1-1-1-122222222-1-1-1-100000000-1-1-1-1-1-1-1-1-1-100000000000022-1-122-1-1-1-1-1-10000
χ302222-1222222-1-1-1222222-1-1-1-1-1-122222222-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1000000000000-2-211-2-21111110000
χ312222-1222222-1-1-1222222-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-100000000-1-11111111100000000000022-1-1-2-2-1-111110000
χ322222-1222222-1-1-1222222-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-100000000-1-111111111000000000000-2-2112211-1-1-1-10000
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χ342222-1-2-222-2-2-1-1-1-2-2-2-22211-1-1112i2i2i2i−2i−2i−2i−2i111100000000-1-1−i−i−i−iiiii000000000000-2211−2i2i-1-1ii−i−i0000
χ352222-1-2-222-2-2-1-1-1-2-2-2-22211-1-111−2i−2i−2i−2i2i2i2i2i111100000000-1-1iiii−i−i−i−i0000000000002-2-1-1−2i2i11ii−i−i0000
χ362222-1-2-222-2-2-1-1-1-2-2-2-22211-1-111−2i−2i−2i−2i2i2i2i2i111100000000-1-1iiii−i−i−i−i000000000000-22112i−2i-1-1−i−iii0000
χ3722-2-222i−2i2-22i−2i2-2-20000002i−2i2-22i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000002i2i−2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
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χ4422-2-222i−2i-22−2i2i2-2-2−2i−2i2i2i-222i−2i-22−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2i−2i2i2i00000000-222ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000000000000000
χ4522-2-22−2i2i2-2−2i2i2-2-2000000−2i2i2-2−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000002i2i−2i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i00-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ4622-2-22−2i2i2-2−2i2i2-2-2000000−2i2i2-2−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000−2i−2i2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ4722-2-22−2i2i2-2−2i2i2-2-2000000−2i2i2-2−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000002i2i−2i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i00-221−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ4822-2-22−2i2i2-2−2i2i2-2-2000000−2i2i2-2−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000−2i−2i2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ4922-2-22−2i2i-222i−2i2-2-22i2i−2i−2i-22−2i2i-222i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132i2i−2i−2i00000000-222ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000000000000000
χ5022-2-22−2i2i-222i−2i2-2-22i2i−2i−2i-22−2i2i-222i−2i−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132i2i−2i−2i00000000-22−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000000000000000
χ5122-2-22−2i2i-222i−2i2-2-2−2i−2i2i2i2-2−2i2i-222i−2i00000000−2i−2i2i2i000000002-20000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ5222-2-22−2i2i-222i−2i2-2-2−2i−2i2i2i2-2−2i2i-222i−2i00000000−2i−2i2i2i000000002-2000000000000−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ5322-2-2-12i−2i-22−2i2i-111−2i−2i2i2i-22−ii1-1i−i−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23ii−i−i000000001-1ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ2300000000000000−i3i3003−3ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000
χ5422-2-2-12i−2i-22−2i2i-111−2i−2i2i2i-22−ii1-1i−i−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23ii−i−i000000001-1ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ2300000000000000i3−i300−33−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000
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χ794-4-444000000-4-44−222222−220000000000000000−222222−22004-4−222222−2200000000000000000000000000000000000000
χ804-4-444000000-4-44−222222−220000000000000000−222222−2200-4422−22−222200000000000000000000000000000000000000
χ818-88-8-40000004-44−4i24i2−4i24i200000000000000002i2−2i22i2−2i20000000000000000000000000000000000000000000000
χ828-88-8-40000004-444i2−4i24i2−4i20000000000000000−2i22i2−2i22i20000000000000000000000000000000000000000000000
χ838-8-88-400000044-442−42−42420000000000000000−222222−220000000000000000000000000000000000000000000000
χ848-8-88-400000044-4−424242−42000000000000000022−22−22220000000000000000000000000000000000000000000000

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