Finite Group Databasebeta

← Group #97104

Character table — Group #97104

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222222222222444444442222444444444444444444442444444488888888
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
χ511111111111111111111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii11-1-111-1-1ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-111−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i11-1-111-1-1−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111ii−i−i−i−iii
χ17222222222222222222222222-2-2-2-2-2-2-2-2-2-22200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-222222222-2-222-2-2-2-200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-22200000000000000000000000000000000
χ2122222222-2-2-2-2222-2-2-22-2000022-2-200002-200000000000000000000002-22-200000000
χ2222222222-2-2-2-2222-2-2-22-2000022-2-200002-20000000000000000000000-22-2200000000
χ2322222222-2-2-2-2222-2-2-22-20000-2-2220000-220000000000000000002-22-2000000000000
χ2422222222-2-2-2-2222-2-2-22-20000-2-2220000-22000000000000000000-22-22000000000000
χ2522222222-2-2-2-2-2-2-2222-22000022-2-20000-220000000000000000002-2-22000000000000
χ2622222222-2-2-2-2-2-2-2222-22000022-2-20000-22000000000000000000-222-2000000000000
χ2722222222-2-2-2-2-2-2-2222-220000-2-22200002-200000000000000000000002-2-2200000000
χ2822222222-2-2-2-2-2-2-2222-220000-2-22200002-20000000000000000000000-222-200000000
χ292222-2-2-2-222-2-2000000002i2i−2i−2i2i−2i2i−2i002-200001+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ302222-2-2-2-222-2-2000000002i2i−2i−2i2i−2i2i−2i002-20000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ312222-2-2-2-222-2-2000000002i2i−2i−2i−2i2i−2i2i00-2200001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ322222-2-2-2-222-2-2000000002i2i−2i−2i−2i2i−2i2i00-220000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ332222-2-2-2-222-2-200000000−2i−2i2i2i2i−2i2i−2i00-2200001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ342222-2-2-2-222-2-200000000−2i−2i2i2i2i−2i2i−2i00-220000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ352222-2-2-2-222-2-200000000−2i−2i2i2i−2i2i−2i2i002-200001−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ362222-2-2-2-222-2-200000000−2i−2i2i2i−2i2i−2i2i002-20000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ3722-2-222-2-22-22-222-22-2-2-222i−2i2i−2i00000000002i−2i000000000000000000000000i2−i2i2−i22−22−2
χ3822-2-222-2-22-22-222-22-2-2-222i−2i2i−2i00000000002i−2i000000000000000000000000−i2i2−i2i2−22−22
χ3922-2-222-2-22-22-222-22-2-2-22−2i2i−2i2i0000000000−2i2i000000000000000000000000i2−i2i2−i2−22−22
χ4022-2-222-2-22-22-222-22-2-2-22−2i2i−2i2i0000000000−2i2i000000000000000000000000−i2i2−i2i22−22−2
χ4122-2-222-2-22-22-2-2-22-2222-22i−2i2i−2i0000000000−2i2i0000000000000000000000002−2−22−i2i2i2−i2
χ4222-2-222-2-22-22-2-2-22-2222-22i−2i2i−2i0000000000−2i2i000000000000000000000000−222−2i2−i2−i2i2
χ4322-2-222-2-22-22-2-2-22-2222-2−2i2i−2i2i00000000002i−2i0000000000000000000000002−2−22i2−i2−i2i2
χ4422-2-222-2-22-22-2-2-22-2222-2−2i2i−2i2i00000000002i−2i000000000000000000000000−222−2−i2i2i2−i2
χ454444-4-4-4-4-4-4440000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ464444-4-4-4-4-4-444000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ4744-4-444-4-4-44-4444-4-444-4-4000000000000000000000000000000000000000000000000
χ4844-4-444-4-4-44-44-4-444-4-444000000000000000000000000000000000000000000000000
χ4944-4-4-4-4444-4-44000000004-4-4400000000000000000000000000000000000000000000
χ5044-4-4-4-4444-4-4400000000-444-400000000000000000000000000000000000000000000
χ5144-4-4-4-444-444-400000000000000004-400000000000000000000000000000000000000
χ5244-4-4-4-444-444-40000000000000000-4400000000000000000000000000000000000000
χ534-44-44-44-4000000044-40-400000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ544-44-44-44-4000000044-40-40000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ554-44-44-44-40000000-4-440400000000000000002-22-2-22-22000000000000000000000000
χ564-44-44-44-40000000-4-44040000000000000000-22-222-22-2000000000000000000000000
χ574-44-4-44-4400004-44000-4000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ584-44-4-44-4400004-44000-400000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ594-44-4-44-440000-44-40004000000000000000002-2-22-222-2000000000000000000000000
χ604-44-4-44-440000-44-4000400000000000000000-222-22-2-22000000000000000000000000
χ614-4-444-4-4400000004-440-40000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ624-4-444-4-4400000004-440-4000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ634-4-444-4-440000000-44-4040000000000000000000000002-22-2-22-220000000000000000
χ644-4-444-4-440000000-44-404000000000000000000000000-22-222-22-20000000000000000
χ654-4-44-444-400004-4-4000400000000000000000000000002-2-22-222-20000000000000000
χ664-4-44-444-400004-4-400040000000000000000000000000-222-22-2-220000000000000000
χ674-4-44-444-40000-444000-400000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ684-4-44-444-40000-444000-40000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000

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