Finite Group Databasebeta

← Group #10827769

Character table — Group #10827769

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11222222222224444444444444444888888888888888881212121216161616161616161616242424242424242424244848
order122222222366644444466666612121212244444412121212121212121212224444612121212121212224444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-11-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-1
χ411111111111111111111111111111-11-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-111
χ5111111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-1-1-111111-11111-1-1-1-1-11-11-1-111-1-11-1
χ6111111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11-11-111-1-111-11
χ7111111111111111-1-1-1-11111111111-11-111-1-111-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-1-1-11111-1-1-11
χ8111111111111111-1-1-1-11111111111-11-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1111-1
χ91111111111111-1-11111111111-1-1-1-11-1111-1-1-1-11111-1-1-1-11111-1-11-1-1111-1-1-11-1111-1-111-1-1
χ101111111111111-1-11111111111-1-1-1-11-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1111-1-11-11-1-1-111-1-111
χ111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-111-1-1-111-1-1-1-1-1-1-1-11111
χ121111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-1-11111111111-1-1-1-1
χ131111111111111-1-1-1-1-1-1111111-1-1-1-11-11-1-111-1-1-1-1-1-111111111-111-1-11-1-1111111-1-1-1-1-1-1-11
χ141111111111111-1-1-1-1-1-1111111-1-1-1-11-11-1-111-1-1-1-1-1-11111-1-1-1-1-111-1-11-1-111-1-1-1-11111111-1
χ151111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111-1-111-111-1-11-11-111-1-1-1-11-1
χ161111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11-1-111-111-1-1-11-11-1-11111-11
χ17222222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ18222222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-22-2-2-222-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ19222222222-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1222-2-2-2-2-1-11111111100002-2-1-1-1-11111000000000000
χ20222222222-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-22-222-2-2-1-1111111110000-221111-1-1-1-1000000000000
χ21222222222-1-1-1-1-2-22222-1-1-1-1-1-111112-2222-2-211-1-1-1-111110000-2-2-111-1-1-111000000000000
χ22222222222-1-1-1-1-2-22222-1-1-1-1-1-11111-2-2-2-2-2-2-211-1-1-1-111110000221-1-1111-1-1000000000000
χ23222222222-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-111112-22-2-222111111-1-1-1-10000-22-111-111-1-1000000000000
χ24222222222-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-11111-2-2-22222111111-1-1-1-100002-21-1-11-1-111000000000000
χ252222-22-2-2-22222002i2i−2i−2i22-2-2-2-2000020-22i−2i00002i2i−2i−2i0000000000200-22i−2i00000000000000
χ262222-22-2-2-22222002i2i−2i−2i22-2-2-2-20000-202−2i2i00002i2i−2i−2i0000000000-2002−2i2i00000000000000
χ272222-22-2-2-2222200−2i−2i2i2i22-2-2-2-2000020-2−2i2i0000−2i−2i2i2i0000000000200-2−2i2i00000000000000
χ282222-22-2-2-2222200−2i−2i2i2i22-2-2-2-20000-2022i−2i0000−2i−2i2i2i0000000000-20022i−2i00000000000000
χ292222-22-2-2-2-1-1-1-1002i2i−2i−2i-1-11111−i3−i3i3i320-22i−2i00−i3i3−i−iii33−3−3000000-1−i3i31−ii3−3000000000000
χ302222-22-2-2-2-1-1-1-1002i2i−2i−2i-1-11111−i3−i3i3i3-202−2i2i00−i3i3−i−iii33−3−30000001i3−i3-1i−i−33000000000000
χ312222-22-2-2-2-1-1-1-1002i2i−2i−2i-1-11111i3i3−i3−i320-22i−2i00i3−i3−i−iii−3−333000000-1i3−i31−ii−33000000000000
χ322222-22-2-2-2-1-1-1-1002i2i−2i−2i-1-11111i3i3−i3−i3-202−2i2i00i3−i3−i−iii−3−3330000001−i3i3-1i−i3−3000000000000
χ332222-22-2-2-2-1-1-1-100−2i−2i2i2i-1-11111−i3−i3i3i320-2−2i2i00−i3i3ii−i−i−3−333000000-1−i3i31i−i−33000000000000
χ342222-22-2-2-2-1-1-1-100−2i−2i2i2i-1-11111−i3−i3i3i3-2022i−2i00−i3i3ii−i−i−3−3330000001i3−i3-1−ii3−3000000000000
χ352222-22-2-2-2-1-1-1-100−2i−2i2i2i-1-11111i3i3−i3−i320-2−2i2i00i3−i3ii−i−i33−3−3000000-1i3−i31i−i3−3000000000000
χ362222-22-2-2-2-1-1-1-100−2i−2i2i2i-1-11111i3i3−i3−i3-2022i−2i00i3−i3ii−i−i33−3−30000001−i3i3-1−ii−33000000000000
χ37222-22-22-2-22-2-22002i−2i2i−2i2-222-2-200000000000002i−2i2i−2i000000000000000000020-22i−2i000000
χ38222-22-22-2-22-2-22002i−2i2i−2i2-222-2-200000000000002i−2i2i−2i0000000000000000000-202−2i2i000000
χ39222-22-22-2-22-2-2200−2i2i−2i2i2-222-2-20000000000000−2i2i−2i2i000000000000000000020-2−2i2i000000
χ40222-22-22-2-22-2-2200−2i2i−2i2i2-222-2-20000000000000−2i2i−2i2i0000000000000000000-2022i−2i000000
χ41222-2-2-2-2222-2-22002-2-222-2-2-22200000000000002-2-22000022-2-20000000000000000002-200
χ42222-2-2-2-2222-2-22002-2-222-2-2-22200000000000002-2-220000-2-222000000000000000000-2200
χ43222-2-2-2-2222-2-2200-222-22-2-2-2220000000000000-222-2000022-2-2000000000000000000-2200
χ44222-2-2-2-2222-2-2200-222-22-2-2-2220000000000000-222-20000-2-2220000000000000000002-200
χ4522-22-2-22-222222220000-2-22-2-2222220-200000-2-2000000002-22-200000000000000002-20000
χ4622-22-2-22-222222220000-2-22-2-2222220-200000-2-200000000-22-220000000000000000-220000
χ4722-22-2-22-222222-2-20000-2-22-2-22-2-2-2-2020000022000000002-22-20000000000000000-220000
χ4822-22-2-22-222222-2-20000-2-22-2-22-2-2-2-202000002200000000-22-2200000000000000002-20000
χ4922-2-222-2-222-2-22000000-22-22-220000000002-20000002-22-22-2-22000000000020-2000000000
χ5022-2-222-2-222-2-22000000-22-22-220000000002-20000002-22-2-222-20000000000-202000000000
χ5122-2-222-2-222-2-22000000-22-22-22000000000-22000000-22-222-2-220000000000-202000000000
χ5222-2-222-2-222-2-22000000-22-22-22000000000-22000000-22-22-222-2000000000020-2000000000
χ53444-44-44-4-4-222-2004i−4i4i−4i-22-2-2220000000000000−2i2i−2i2i000000000000000000000000000000
χ54444-44-44-4-4-222-200−4i4i−4i4i-22-2-22200000000000002i−2i2i−2i000000000000000000000000000000
χ55444-4-4-4-444-222-2004-4-44-2222-2-20000000000000-222-2000000000000000000000000000000
χ56444-4-4-4-444-222-200-444-4-2222-2-200000000000002-2-22000000000000000000000000000000
χ5744-444-4-44-44444000000-4-4-444-400000000000000000000000000000000000000000000000
χ5844-444-4-44-4-2-2-2-2000000222-2-22−2i3−2i32i32i300000002i3−2i30000000000000000000000000000000000
χ5944-444-4-44-4-2-2-2-2000000222-2-222i32i3−2i3−2i30000000−2i32i30000000000000000000000000000000000
χ6044-44-4-44-44-2-2-2-244000022-222-2-2-2-2-20-400000220000000000000000000000000000000000
χ6144-44-4-44-44-2-2-2-2-4-4000022-222-222220400000-2-20000000000000000000000000000000000
χ6244-4-444-4-44-222-20000002-22-22-20000000004-4000000-22-2200000000000000000000000000
χ6344-4-444-4-44-222-20000002-22-22-2000000000-440000002-22-200000000000000000000000000
χ6444-4-4-4444-44-4-44000000-444-44-400000000000000000000000000000000000000000000000
χ6544-4-4-4444-4-222-20000002-2-22-220000000000000000023−23−232300000000000000000000000000
χ6644-4-4-4444-4-222-20000002-2-22-2200000000000000000−232323−2300000000000000000000000000
χ678-80000000800-84i−4i00000000004i−4i4i−4i0000000000000000000000000000000000000000000
χ688-80000000800-8−4i4i0000000000−4i4i−4i4i0000000000000000000000000000000000000000000
χ698-80000000-4−4i34i344i−4i00000000004ζ7−4ζ74ζ11−4ζ110000000000000000000000000000000000000000000
χ708-80000000-4−4i34i34−4i4i0000000000−4ζ74ζ7−4ζ114ζ110000000000000000000000000000000000000000000
χ718-80000000-44i3−4i344i−4i00000000004ζ11−4ζ114ζ7−4ζ70000000000000000000000000000000000000000000
χ728-80000000-44i3−4i34−4i4i0000000000−4ζ114ζ11−4ζ74ζ70000000000000000000000000000000000000000000

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