Finite Group Databasebeta

← Group #10695504

Character table — Group #10695504

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222224444444444444448888888888888816161616161616161616161624242424484848484848
order12222234466622444666612121212121244446121212121212121212448812121212242424242244244488
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ5111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1
χ6111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-111
χ7111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1
χ8111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111
χ9222222222222-2-22-2-222-2-222-2-2-2-20000-22000000002-20022-2-200000000000000
χ10222222222222-2-22-2-222-2-222-2-2-2-20000-2200000000-2200-2-22200000000000000
χ112222222-2-222222-2-2-22222-2-2-2-2-2-200002-2000000000000000000000000002-200
χ122222222-2-222222-2-2-22222-2-2-2-2-2-200002-200000000000000000000000000-2200
χ132222222-2-2222-2-2-22222-2-2-2-222220000-2-20000000000000000000022-2-2000000
χ142222222-2-2222-2-2-22222-2-2-2-222220000-2-200000000000000000000-2-222000000
χ15222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ16222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ17222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-111110000000000
χ18222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-10000000000
χ19222222-122-1-1-1-2-22-2-2-1-111-1-1111100001-13333−3−3−3−32-200-1-11133−3−30000000000
χ20222222-122-1-1-1-2-22-2-2-1-111-1-1111100001-13333−3−3−3−3-220011-1-1−3−3330000000000
χ21222222-122-1-1-1-2-22-2-2-1-111-1-1111100001-1−3−3−3−333332-200-1-111−3−3330000000000
χ22222222-122-1-1-1-2-22-2-2-1-111-1-1111100001-1−3−3−3−33333-220011-1-133−3−30000000000
χ232222-2-22222222-2-2-22-2-2-2-222-2-22200002-20000000000000000000000002-20000
χ242222-2-22222222-2-2-22-2-2-2-222-2-22200002-2000000000000000000000000-220000
χ252222-2-2222222-22-22-2-2-2222222-2-20000-2-200000000000000000000000000002-2
χ262222-2-2222222-22-22-2-2-2222222-2-20000-2-20000000000000000000000000000-22
χ272222-2-22-2-22222-222-2-2-2-2-2-2-222-2-22i2i−2i−2i222i2i−2i−2i2i2i−2i−2i0000000000000000000000
χ282222-2-22-2-22222-222-2-2-2-2-2-2-222-2-2−2i−2i2i2i22−2i−2i2i2i−2i−2i2i2i0000000000000000000000
χ292222-2-22-2-2222-222-22-2-222-2-2-2-2220000-2200000000002-200002-22-20000000000
χ302222-2-22-2-2222-222-22-2-222-2-2-2-2220000-220000000000-220000-22-220000000000
χ312222-2-2-1-2-2-1-1-12-222-2111111-1-1112i2i−2i−2i-1-1−i−iii−i−iii0000−i3i3−i3i33−3−330000000000
χ322222-2-2-1-2-2-1-1-12-222-2111111-1-1112i2i−2i−2i-1-1−i−iii−i−iii0000i3−i3i3−i3−333−30000000000
χ332222-2-2-1-2-2-1-1-12-222-2111111-1-111−2i−2i2i2i-1-1ii−i−iii−i−i0000−i3i3−i3i3−333−30000000000
χ342222-2-2-1-2-2-1-1-12-222-2111111-1-111−2i−2i2i2i-1-1ii−i−iii−i−i0000i3−i3i3−i33−3−330000000000
χ352222-2-2-1-2-2-1-1-1-222-2211-1-11111-1-100001-1−i3−i3i3i3i3i3−i3−i3002-2−i3i3i3−i3-11-110000000000
χ362222-2-2-1-2-2-1-1-1-222-2211-1-11111-1-100001-1−i3−i3i3i3i3i3−i3−i300-22i3−i3−i3i31-11-10000000000
χ372222-2-2-1-2-2-1-1-1-222-2211-1-11111-1-100001-1i3i3−i3−i3−i3−i3i3i3002-2i3−i3−i3i3-11-110000000000
χ382222-2-2-1-2-2-1-1-1-222-2211-1-11111-1-100001-1i3i3−i3−i3−i3−i3i3i300-22−i3i3i3−i31-11-10000000000
χ39444444-2-4-4-2-2-244-4-4-4-2-2-2-22222220000-22000000000000000000000000000000
χ40444444-2-4-4-2-2-2-4-4-444-2-22222-2-2-2-2000022000000000000000000000000000000
χ414444-4-4-244-2-2-24-4-4-442222-2-222-2-20000-22000000000000000000000000000000
χ424444-4-4-244-2-2-2-44-44-422-2-2-2-2-2-222000022000000000000000000000000000000
χ434-44-44-4400-44-4000004-4000000002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ444-44-44-4400-44-4000004-400000000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ454-44-44-4-2002-2200000-22000023−2323−232i−2i2i−2i00−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000000000
χ464-44-44-4-2002-2200000-22000023−2323−23−2i2i−2i2i00ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000000000000000000
χ474-44-44-4-2002-2200000-220000−2323−23232i−2i2i−2i00ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000000000000000000
χ484-44-44-4-2002-2200000-220000−2323−2323−2i2i−2i2i00−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000000000000000000
χ494-44-4-44400-44-400000-44000000002-2-22002-2-222-2-220000000000000000000000
χ504-44-4-44400-44-400000-4400000000-222-200-222-2-222-20000000000000000000000
χ514-44-4-44-2002-22000002-2000023−23−23232-2-2200−1−31+31+3−1−3−1+31−31−3−1+30000000000000000000000
χ524-44-4-44-2002-22000002-2000023−23−2323-222-2001+3−1−3−1−31+31−3−1+3−1+31−30000000000000000000000
χ534-44-4-44-2002-22000002-20000−232323−232-2-2200−1+31−31−3−1+3−1−31+31+3−1−30000000000000000000000
χ544-44-4-44-2002-22000002-20000−232323−23-222-2001−3−1+3−1+31−31+3−1−3−1−31+30000000000000000000000
χ554-4-440044-4-4-440000000004-40000000000000000000000000000002-22-2000000
χ564-4-440044-4-4-440000000004-4000000000000000000000000000000-22-22000000
χ574-4-44004-44-4-44000000000-440000000000000000000000000000002-2-22000000
χ584-4-44004-44-4-44000000000-44000000000000000000000000000000-222-2000000
χ5988-8-8008008-8-8000000000000000000000000000000000000000000000000000
χ6088-8-800-400-4440000000−4i34i3000000000000000000000000000000000000000000
χ6188-8-800-400-44400000004i3−4i3000000000000000000000000000000000000000000
χ628-8-8800-48-844-4000000000-440000000000000000000000000000000000000000
χ638-8-8800-4-8844-40000000004-40000000000000000000000000000000000000000

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