Finite Group Databasebeta

← Group #10693003

Character table — Group #10693003

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222224444444444488888888888888888888888888161616161616242424242424242448484848
order1222222234444666121212122446666121212122244444466666121212121212121212121212128824242424224444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ411111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ9111111-1-11-1-1-1-1111-1-1-1-1-11111-1-111-1-111-1-1ii−i−i-111111-1-1-1-1iiii−i−i−i−ii−iii−i−i1-11-1ii−i−i1-1i−i
χ10111111-1-11-1-1-1-1111-1-1-1-1-11111-1-111-1-111-1-1ii−i−i-111111-1-1-1-1iiii−i−i−i−ii−iii−i−i-11-11−i−iii-11−ii
χ11111111-1-11-1-1-1-1111-1-1-1-1-11111-1-111-1-111-1-1−i−iii-111111-1-1-1-1−i−i−i−iiiii−ii−i−iii1-11-1−i−iii1-1−ii
χ12111111-1-11-1-1-1-1111-1-1-1-1-11111-1-111-1-111-1-1−i−iii-111111-1-1-1-1−i−i−i−iiiii−ii−i−iii-11-11ii−i−i-11i−i
χ13111111-1-11-1-1-1-1111-1-1-1-1-11111-1-111-1-1-1-111ii−i−i-1-1-1-1-111111iiii−i−i−i−i−ii−i−iii1-11-1ii−i−i-11−ii
χ14111111-1-11-1-1-1-1111-1-1-1-1-11111-1-111-1-1-1-111ii−i−i-1-1-1-1-111111iiii−i−i−i−i−ii−i−iii-11-11−i−iii1-1i−i
χ15111111-1-11-1-1-1-1111-1-1-1-1-11111-1-111-1-1-1-111−i−iii-1-1-1-1-111111−i−i−i−iiiiii−iii−i−i1-11-1−i−iii-11i−i
χ16111111-1-11-1-1-1-1111-1-1-1-1-11111-1-111-1-1-1-111−i−iii-1-1-1-1-111111−i−i−i−iiiiii−iii−i−i-11-11ii−i−i1-1−ii
χ17222222222-2-2-2-2222-2-2-2-22-2-22222-2-2-2-20000000020000-200000000000000000022-2-200000000
χ18222222222-2-2-2-2222-2-2-2-22-2-22222-2-2-2-20000000020000-2000000000000000000-2-22200000000
χ1922222222-12222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ2022222222-12222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-21111000000000000
χ2122222222-12222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-22222-11111-11111-1-1-1-1-1-1-1-1-2-21111000000000000
χ2222222222-12222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-11111-111111111111122-1-1-1-1000000000000
χ23222222-2-2222222222222-2-2-222-2-2-2-22200000000-20000-20000000000000000002-2-2200000000
χ24222222-2-2222222222222-2-2-222-2-2-2-22200000000-20000-2000000000000000000-222-200000000
χ25222222-2-2-1-2-2-2-2-1-1-11111-222-1-111-1-11122-2-22i2i−2i−2i1-1-1-1-1-11111−i−i−i−iiiii2i−2i−i−iii000000000000
χ26222222-2-2-1-2-2-2-2-1-1-11111-222-1-111-1-11122-2-2−2i−2i2i2i1-1-1-1-1-11111iiii−i−i−i−i−2i2iii−i−i000000000000
χ27222222-2-2-1-2-2-2-2-1-1-11111-222-1-111-1-111-2-2222i2i−2i−2i11111-1-1-1-1-1−i−i−i−iiiii−2i2iii−i−i000000000000
χ28222222-2-2-1-2-2-2-2-1-1-11111-222-1-111-1-111-2-222−2i−2i2i2i11111-1-1-1-1-1iiii−i−i−i−i2i−2i−i−iii000000000000
χ292222-2-222222-2-22222222-22-2-2-22222-2-200002-22-2-20000-2000022-2-222-2-2000000000000000000
χ302222-2-222222-2-22222222-22-2-2-22222-2-20000-22-22-20000-20000-2-222-2-222000000000000000000
χ312222-2-2222-2-222222-2-2-2-2-2-22-2-222-2-22200000000-20000200000000000000000000002-22-20000
χ322222-2-2222-2-222222-2-2-2-2-2-22-2-222-2-22200000000-2000020000000000000000000000-22-220000
χ332222-2-222-122-2-2-1-1-1-1-1-1-1-22-211-1-1-1-11100002-22-21−i3−i3i3i31−i3−i3i3i3-1-111-1-11100−i3i3−i3i3000000000000
χ342222-2-222-122-2-2-1-1-1-1-1-1-1-22-211-1-1-1-11100002-22-21i3i3−i3−i31i3i3−i3−i3-1-111-1-11100i3−i3i3−i3000000000000
χ352222-2-222-122-2-2-1-1-1-1-1-1-1-22-211-1-1-1-1110000-22-221−i3−i3i3i31−i3−i3i3i311-1-111-1-100i3−i3i3−i3000000000000
χ362222-2-222-122-2-2-1-1-1-1-1-1-1-22-211-1-1-1-1110000-22-221i3i3−i3−i31i3i3−i3−i311-1-111-1-100−i3i3−i3i3000000000000
χ372222-2-2-2-2222-2-222222222-22-2-2-2-2-2-2-2-20000000020000200000000000000000000002i−2i−2i2i0000
χ382222-2-2-2-2222-2-222222222-22-2-2-2-2-2-2-2-2000000002000020000000000000000000000−2i2i2i−2i0000
χ392222-2-2-2-22-2-222222-2-2-2-222-2-2-2-2-2222200002i−2i−2i2i20000-200002i2i−2i−2i−2i−2i2i2i000000000000000000
χ402222-2-2-2-22-2-222222-2-2-2-222-2-2-2-2-222220000−2i2i2i−2i20000-20000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ412222-2-2-2-2-1-2-222-1-1-1111122-21111-1-1-1-100002i−2i−2i2i-1−i3−i3i3i31i3i3−i3−i3−i−iiiii−i−i003−3−33000000000000
χ422222-2-2-2-2-1-2-222-1-1-1111122-21111-1-1-1-100002i−2i−2i2i-1i3i3−i3−i31−i3−i3i3i3−i−iiiii−i−i00−333−3000000000000
χ432222-2-2-2-2-1-2-222-1-1-1111122-21111-1-1-1-10000−2i2i2i−2i-1−i3−i3i3i31i3i3−i3−i3ii−i−i−i−iii00−333−3000000000000
χ442222-2-2-2-2-1-2-222-1-1-1111122-21111-1-1-1-10000−2i2i2i−2i-1i3i3−i3−i31−i3−i3i3i3ii−i−i−i−iii003−3−33000000000000
χ4544444444-2-4-4-4-4-2-2-222224-4-4-2-2-2-2222200000000-200002000000000000000000000000000000
χ46444444-4-4-24444-2-2-2-2-2-2-2-4-4-4-2-22222-2-200000000200002000000000000000000000000000000
χ474444-4-444-2-4-444-2-2-22222-4-4422-2-222-2-20000000020000-2000000000000000000000000000000
χ484444-4-4-4-4-244-4-4-2-2-2-2-2-2-24-442222222200000000-20000-2000000000000000000000000000000
χ4944-4-44-40044i−4i4i−4i4-4-44i4i−4i−4i0004-400004i−4i00000000000000000000000000000000000000000000
χ5044-4-44-4004−4i4i−4i4i4-4-4−4i−4i4i4i0004-40000−4i4i00000000000000000000000000000000000000000000
χ5144-4-44-400-24i−4i4i−4i-222−2i−2i2i2i000-220000−2i2i000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11000000000000000000
χ5244-4-44-400-24i−4i4i−4i-222−2i−2i2i2i000-220000−2i2i000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11000000000000000000
χ5344-4-44-400-2−4i4i−4i4i-2222i2i−2i−2i000-2200002i−2i000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11000000000000000000
χ5444-4-44-400-2−4i4i−4i4i-2222i2i−2i−2i000-2200002i−2i000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11000000000000000000
χ5544-4-4-440044i−4i−4i4i4-4-44i4i−4i−4i000-440000−4i4i00000000000000000000000000000000000000000000
χ5644-4-4-44004−4i4i4i−4i4-4-4−4i−4i4i4i000-4400004i−4i00000000000000000000000000000000000000000000
χ5744-4-4-4400-24i−4i−4i4i-222−2i−2i2i2i0002-200002i−2i000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11000000000000000000
χ5844-4-4-4400-24i−4i−4i4i-222−2i−2i2i2i0002-200002i−2i000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11000000000000000000
χ5944-4-4-4400-2−4i4i4i−4i-2222i2i−2i−2i0002-20000−2i2i000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11000000000000000000
χ6044-4-4-4400-2−4i4i4i−4i-2222i2i−2i−2i0002-20000−2i2i000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11000000000000000000
χ614-44-4004-440000-4-440000000004-400002-22-2000002-22-202-22-200000000000000000000000000
χ624-44-4004-440000-4-440000000004-40000-22-2200000-22-220-22-2200000000000000000000000000
χ634-44-4004-4-2000022-2−2i32i3−2i32i300000-22−2i32i3002-22-200000−1−i31+i3−1+i31−i30−1−i31+i3−1+i31−i300000000000000000000000000
χ644-44-4004-4-2000022-2−2i32i3−2i32i300000-22−2i32i300-22-22000001+i3−1−i31−i3−1+i301+i3−1−i31−i3−1+i300000000000000000000000000
χ654-44-4004-4-2000022-22i3−2i32i3−2i300000-222i3−2i3002-22-200000−1+i31−i3−1−i31+i30−1+i31−i3−1−i31+i300000000000000000000000000
χ664-44-4004-4-2000022-22i3−2i32i3−2i300000-222i3−2i300-22-22000001−i3−1+i31+i3−1−i301−i3−1+i31+i3−1−i300000000000000000000000000
χ674-44-400-4440000-4-44000000000-4400002-2-22000002-22-20-22-2200000000000000000000000000
χ684-44-400-4440000-4-44000000000-440000-222-200000-22-2202-22-200000000000000000000000000
χ694-44-400-44-2000022-2−2i32i3−2i32i3000002-22i3−2i3002-2-2200000−1+i31−i3−1−i31+i301−i3−1+i31+i3−1−i300000000000000000000000000
χ704-44-400-44-2000022-2−2i32i3−2i32i3000002-22i3−2i300-222-2000001−i3−1+i31+i3−1−i30−1+i31−i3−1−i31+i300000000000000000000000000
χ714-44-400-44-2000022-22i3−2i32i3−2i3000002-2−2i32i3002-2-2200000−1−i31+i3−1+i31−i301+i3−1−i31−i3−1+i300000000000000000000000000
χ724-44-400-44-2000022-22i3−2i32i3−2i3000002-2−2i32i300-222-2000001+i3−1−i31−i3−1+i30−1−i31+i3−1+i31−i300000000000000000000000000
χ738-8-88000080000-88-800000000000000000000000000000000000000000000000000000000000
χ748-8-880000-400004-4443−43−43430000000000000000000000000000000000000000000000000000000
χ758-8-880000-400004-44−434343−430000000000000000000000000000000000000000000000000000000

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