Finite Group Databasebeta

← Group #100970

Character table — Group #100970

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444422444488888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-111-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-111-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ12111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222222222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-222-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ19222222222222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-22200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-200000000000000000000000000000000
χ2122222222-2-2-2-222220000-2-2000022-2-2002-2000000000022-2-222-2-20000000000000000
χ2222222222-2-2-2-222220000-2-2000022-2-2002-20000000000-2-222-2-2220000000000000000
χ2322222222-2-2-2-222220000-2-20000-2-22200-220022-2-222-2-2000000000000000000000000
χ2422222222-2-2-2-222220000-2-20000-2-22200-2200-2-222-2-222000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2000022000022-2-200-22002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-2000022000022-2-200-2200−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-20000220000-2-222002-200000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-20000220000-2-222002-20000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ29222-2-2-2-222-22-22i2i−2i−2i2i2i−2i−2i2i−2i22-2-200000000000000000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ30222-2-2-2-222-22-22i2i−2i−2i2i2i−2i−2i2i−2i22-2-20000000000000000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ31222-2-2-2-222-22-22i2i−2i−2i−2i−2i2i2i2i−2i-2-22200000000000000000000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i
χ32222-2-2-2-222-22-22i2i−2i−2i−2i−2i2i2i2i−2i-2-2220000000000000000000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i
χ33222-2-2-2-222-22-2−2i−2i2i2i2i2i−2i−2i−2i2i-2-22200000000000000000000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i
χ34222-2-2-2-222-22-2−2i−2i2i2i2i2i−2i−2i−2i2i-2-2220000000000000000000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i
χ35222-2-2-2-222-22-2−2i−2i2i2i−2i−2i2i2i−2i2i22-2-200000000000000000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ36222-2-2-2-222-22-2−2i−2i2i2i−2i−2i2i2i−2i2i22-2-20000000000000000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ3722-2-2-222-22-2-2200002i−2i2i−2i0000002i−2i2i−2i00002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ3822-2-2-222-22-2-2200002i−2i2i−2i0000002i−2i2i−2i00002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ3922-2-2-222-22-2-2200002i−2i2i−2i000000−2i2i−2i2i0000-221−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ4022-2-2-222-22-2-2200002i−2i2i−2i000000−2i2i−2i2i0000-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ4122-2-2-222-22-2-220000−2i2i−2i2i0000002i−2i2i−2i0000-221+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ4222-2-2-222-22-2-220000−2i2i−2i2i0000002i−2i2i−2i0000-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ4322-2-2-222-22-2-220000−2i2i−2i2i000000−2i2i−2i2i00002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ4422-2-2-222-22-2-220000−2i2i−2i2i000000−2i2i−2i2i00002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ4522-2-2-222-2-222-200000000002i−2i2i−2i2i−2i−2i2i2-200001−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ4622-2-2-222-2-222-200000000002i−2i2i−2i2i−2i−2i2i2-20000−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ4722-2-2-222-2-222-200000000002i−2i2i−2i−2i2i2i−2i-2200001+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ4822-2-2-222-2-222-200000000002i−2i2i−2i−2i2i2i−2i-220000−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ4922-2-2-222-2-222-20000000000−2i2i−2i2i2i−2i−2i2i-2200001−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ5022-2-2-222-2-222-20000000000−2i2i−2i2i2i−2i−2i2i-220000−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ5122-2-2-222-2-222-20000000000−2i2i−2i2i−2i2i2i−2i2-200001+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ5222-2-2-222-2-222-20000000000−2i2i−2i2i−2i2i2i−2i2-20000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ53444-4-4-4-44-44-444i4i−4i−4i0000−4i4i0000000000000000000000000000000000000000000000
χ54444-4-4-4-44-44-44−4i−4i4i4i00004i−4i0000000000000000000000000000000000000000000000
χ5544-444-4-4-444-4-400004-4-44000000000000000000000000000000000000000000000000
χ5644-444-4-4-444-4-40000-444-4000000000000000000000000000000000000000000000000
χ5744-444-4-4-4-4-44400000000004i−4i−4i4i000000000000000000000000000000000000000000
χ5844-444-4-4-4-4-4440000000000−4i4i4i−4i000000000000000000000000000000000000000000
χ594-444-44-4-400004-44-40000000000000000000000000000000000002i−2i2i−2i000000000000
χ604-444-44-4-400004-44-4000000000000000000000000000000000000−2i2i−2i2i000000000000
χ614-444-44-4-40000-44-440000000000000000000000000000000000002i−2i−2i2i000000000000
χ624-444-44-4-40000-44-44000000000000000000000000000000000000−2i2i2i−2i000000000000
χ634-44-44-44-400004i−4i−4i4i00000000000000000000000000000000000000002-22i−2i00000000
χ644-44-44-44-400004i−4i−4i4i0000000000000000000000000000000000000000-22−2i2i00000000
χ654-44-44-44-40000−4i4i4i−4i00000000000000000000000000000000000000002-2−2i2i00000000
χ664-44-44-44-40000−4i4i4i−4i0000000000000000000000000000000000000000-222i−2i00000000
χ678-8-88-8-888000000000000000000000000000000000000000000000000000000000000
χ688-8-8-888-88000000000000000000000000000000000000000000000000000000000000

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