Finite Group Databasebeta

← Group #130621

Character table — Group #130621

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111222244444444444444488888888888881616161616161616161616161632323232
order12222244222244444444444224444444444424444444444448888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111-1-1-1-1-1-1111-1-1111111-1-1-1-1-1iiii−i−i−i−iii−i−i
χ41111111111111111111-1-1-1-1-1-1111-1-1111111-1-1-1-1-1−i−i−i−iiiii−i−iii
χ5111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11-11-1
χ6111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-11-11
χ7111111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11-1-111ii−i−i−i−iiii−i−ii
χ8111111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11-1-111−i−iiiii−i−i−iii−i
χ911111111-1-1-1-111111111111111-1-11111-1-1-1-11-1-1-1-111111111-1-1-1-1
χ1011111111-1-1-1-111111111111111-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111
χ1111111111-1-1-1-11111111-1-1-1-1-1-11-1-1-1-111-1-1-1-1-11111iiii−i−i−i−i−i−iii
χ1211111111-1-1-1-11111111-1-1-1-1-1-11-1-1-1-111-1-1-1-1-11111−i−i−i−iiiiiii−i−i
χ1311111111-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-11111-1-1-11111-1-111-1-1-11-11
χ1411111111-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-11111-1-1-111-1-111-1-1111-11-1
χ1511111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11-1-111-1-11111111-1-1ii−i−i−i−iii−iii−i
χ1611111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11-1-111-1-11111111-1-1−i−iiiii−i−ii−i−ii
χ17222222222222-2-22000022-2-22-2-2-2-20000000002-200000000000000
χ18222222222222-2-220000-2-222-22-2-2-2000000000-2200000000000000
χ1922222222-2-2-2-2-2-22000022-2-22-2-222000000000-2200000000000000
χ2022222222-2-2-2-2-2-220000-2-222-22-2220000000002-200000000000000
χ21222222-2-2000022-222222222-2-2-20022-2-20000-20000000000000000
χ22222222-2-2000022-22222-2-2-2-222-200-2-2-2-2000020000000000000000
χ23222222-2-2000022-2-2-2-2-22222-2-2-200-2-222000020000000000000000
χ24222222-2-2000022-2-2-2-2-2-2-2-2-222-20022220000-20000000000000000
χ25222222-2-20000-2-2-2000022-2-2-22200000022-2-20002-2000000000000
χ26222222-2-20000-2-2-2000022-2-2-222000000-2-222000-22000000000000
χ27222222-2-20000-2-2-20000-2-2222-2200000022-2-2000-22000000000000
χ28222222-2-20000-2-2-20000-2-2222-22000000-2-2220002-2000000000000
χ292-22-2-220000002-2022-2-22i−2i2i−2i000002i−2i000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ302-22-2-220000002-2022-2-22i−2i2i−2i000002i−2i00000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ312-22-2-220000002-2022-2-2−2i2i−2i2i00000−2i2i000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ322-22-2-220000002-2022-2-2−2i2i−2i2i00000−2i2i00000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ332-22-2-220000002-20-2-2222i−2i2i−2i00000−2i2i000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000
χ342-22-2-220000002-20-2-2222i−2i2i−2i00000−2i2i00000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000
χ352-22-2-220000002-20-2-222−2i2i−2i2i000002i−2i000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000
χ362-22-2-220000002-20-2-222−2i2i−2i2i000002i−2i00000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000
χ374444-4-44444-4-400-400000000000000000000000000000000000000
χ384444-4-444-4-44400-400000000000000000000000000000000000000
χ394444-4-4-4-40000004000000000004-40000000000000000000000000
χ404444-4-4-4-4000000400000000000-440000000000000000000000000
χ414-44-4-44000000-44000004i−4i−4i4i000000000000000000000000000000
χ424-44-4-44000000-4400000−4i4i4i−4i000000000000000000000000000000
χ434-4-44004-4004-40002-22-2000000000002-22-22-200000000000000000
χ444-4-44004-4004-4000-22-2200000000000-22-22-2200000000000000000
χ454-4-44004-400-440002-22-2000000000002-2-22-2200000000000000000
χ464-4-44004-400-44000-22-2200000000000-222-22-200000000000000000
χ474-4-4400-444-4000002-22-200000000000-222-2-2200000000000000000
χ484-4-4400-444-400000-22-22000000000002-2-222-200000000000000000
χ494-4-4400-44-44000002-22-200000000000-22-222-200000000000000000
χ504-4-4400-44-4400000-22-22000000000002-22-2-2200000000000000000
χ5188-8-8000000000004-4-440000000000000000000000000000000000
χ5288-8-800000000000-444-40000000000000000000000000000000000
χ538-88-88-800000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).