Finite Group Databasebeta

← Group #116398

Character table — Group #116398

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12224444222222444444444444444444444444444444444444444444444444442444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-1-1-1-111-1111111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−i11-1-1ii−i−i
χ101111-1-1-1-1-1-1-111-1111111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111−i−iii-1-111−i−iii
χ111111-1-1-1-1-1-1-111-1111111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii11-1-1−i−iii
χ121111-1-1-1-1-1-1-111-1111111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111ii−i−i-1-111ii−i−i
χ131111-1-1-1-1-1-1-111-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii11-1-1ii−i−i-1-111−i−iii
χ141111-1-1-1-1-1-1-111-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii-1-111−i−iii11-1-1ii−i−i
χ151111-1-1-1-1-1-1-111-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−iii-1-111ii−i−i
χ161111-1-1-1-1-1-1-111-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i11-1-1−i−iii
χ17222222222222222222-2-222-2-2-2-2-2-2-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ18222222222222222222-2-222-2-2-2-2-2-2-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ192222222222-2-2-2-222-2-222-2-2-2-2-2-2222-22-200000000000000000000000000000000000000002i−2i2i−2i0000
χ202222222222-2-2-2-222-2-222-2-2-2-2-2-2222-22-20000000000000000000000000000000000000000−2i2i−2i2i0000
χ212222222222-2-2-2-222-2-2-2-2-2-22222-2-2-22-22000000000000000000000000000000000000000000002i−2i2i−2i
χ222222222222-2-2-2-222-2-2-2-2-2-22222-2-2-22-2200000000000000000000000000000000000000000000−2i2i−2i2i
χ2322222222-2-22-2-22-2-22222-2-2-2-2-2-222-22-22000000000000000000000000000000002-22-2000000000000
χ2422222222-2-22-2-22-2-22222-2-2-2-2-2-222-22-2200000000000000000000000000000000-22-22000000000000
χ2522222222-2-22-2-22-2-222-2-2-2-22222-2-22-22-20000000000000000000000000000000000002-22-200000000
χ2622222222-2-22-2-22-2-222-2-2-2-22222-2-22-22-2000000000000000000000000000000000000-22-2200000000
χ2722222222-2-2-222-2-2-2-2-22222222222-2-2-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2822222222-2-2-222-2-2-2-2-22222222222-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2922222222-2-2-222-2-2-2-2-2-2-222-2-2-2-2-2-222220000000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ3022222222-2-2-222-2-2-2-2-2-2-222-2-2-2-2-2-22222000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ312222-2-2-2-2222222-2-2-2-222-2-2-2-222-2-2-2-2222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ322222-2-2-2-2222222-2-2-2-222-2-2-2-222-2-2-2-222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ332222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-22222-2-200000000000000000000000022-2-2-2-2220000000000000000
χ342222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-22222-2-2000000000000000000000000-2-22222-2-20000000000000000
χ352222-2-2-2-222-2-2-2-2-2-222222222-2-2-2-2-222-2000000000000000000000000000000002-2-22000000000000
χ362222-2-2-2-222-2-2-2-2-2-222222222-2-2-2-2-222-200000000000000000000000000000000-222-2000000000000
χ372222-2-2-2-222-2-2-2-2-2-222-2-222-2-222222-2-220000000000000000000000000000000000002i−2i−2i2i00000000
χ382222-2-2-2-222-2-2-2-2-2-222-2-222-2-222222-2-22000000000000000000000000000000000000−2i2i2i−2i00000000
χ392222-2-2-2-2-2-22-2-2222-2-2222222-2-2-2-22-2-2200000000000000000000000000000000000000002i−2i−2i2i0000
χ402222-2-2-2-2-2-22-2-2222-2-2222222-2-2-2-22-2-220000000000000000000000000000000000000000−2i2i2i−2i0000
χ412222-2-2-2-2-2-22-2-2222-2-2-2-222-2-22222-222-2000000000000000000000000000000000000000000002-2-22
χ422222-2-2-2-2-2-22-2-2222-2-2-2-222-2-22222-222-200000000000000000000000000000000000000000000-222-2
χ432222-2-2-2-2-2-2-222-22222-2-2-2-222-2-222-2-22200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ442222-2-2-2-2-2-2-222-22222-2-2-2-222-2-222-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ4522-2-22i2i−2i−2i0002-2000002-22i−2i2i−2i2-22i−2i000000002i2i−2i−2i000022-2-21+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ4622-2-22i2i−2i−2i0002-2000002-22i−2i2i−2i2-22i−2i000000002i2i−2i−2i000022-2-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ4722-2-22i2i−2i−2i0002-2000002-22i−2i2i−2i2-22i−2i00000000−2i−2i2i2i0000-2-2221+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ4822-2-22i2i−2i−2i0002-2000002-22i−2i2i−2i2-22i−2i00000000−2i−2i2i2i0000-2-222−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ4922-2-22i2i−2i−2i0002-200000-222i−2i−2i2i-22−2i2i000022-2-200002i2i−2i−2i00001+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ5022-2-22i2i−2i−2i0002-200000-222i−2i−2i2i-22−2i2i000022-2-200002i2i−2i−2i0000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ5122-2-22i2i−2i−2i0002-200000-222i−2i−2i2i-22−2i2i0000-2-2220000−2i−2i2i2i00001+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ5222-2-22i2i−2i−2i0002-200000-222i−2i−2i2i-22−2i2i0000-2-2220000−2i−2i2i2i0000−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ5322-2-2−2i−2i2i2i0002-2000002-2−2i2i−2i2i2-2−2i2i000000002i2i−2i−2i0000-2-2221−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ5422-2-2−2i−2i2i2i0002-2000002-2−2i2i−2i2i2-2−2i2i000000002i2i−2i−2i0000-2-222−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ5522-2-2−2i−2i2i2i0002-2000002-2−2i2i−2i2i2-2−2i2i00000000−2i−2i2i2i000022-2-21−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ5622-2-2−2i−2i2i2i0002-2000002-2−2i2i−2i2i2-2−2i2i00000000−2i−2i2i2i000022-2-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ5722-2-2−2i−2i2i2i0002-200000-22−2i2i2i−2i-222i−2i000022-2-20000−2i−2i2i2i00001−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ5822-2-2−2i−2i2i2i0002-200000-22−2i2i2i−2i-222i−2i000022-2-20000−2i−2i2i2i0000−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ5922-2-2−2i−2i2i2i0002-200000-22−2i2i2i−2i-222i−2i0000-2-22200002i2i−2i−2i00001−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ6022-2-2−2i−2i2i2i0002-200000-22−2i2i2i−2i-222i−2i0000-2-22200002i2i−2i−2i0000−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ6144-4-44i4i−4i−4i000-44000004-4−4i4i−4i4i-444i−4i0000000000000000000000000000000000000000000000000000
χ6244-4-44i4i−4i−4i000-4400000-44−4i4i4i−4i4-4−4i4i0000000000000000000000000000000000000000000000000000
χ6344-4-4−4i−4i4i4i000-44000004-44i−4i4i−4i-44−4i4i0000000000000000000000000000000000000000000000000000
χ6444-4-4−4i−4i4i4i000-4400000-444i−4i−4i4i4-44i−4i0000000000000000000000000000000000000000000000000000
χ654-44-44-44-400400-4004-4000000000000002-22-22-22-22-22-22-22-200000000000000000000000000000000
χ664-44-44-44-400400-4004-400000000000000-22-22-22-22-22-22-22-2200000000000000000000000000000000
χ674-44-44-44-400-400400-44000000000000002-22-2-22-222-22-2-22-2200000000000000000000000000000000
χ684-44-44-44-400-400400-4400000000000000-22-222-22-2-22-222-22-200000000000000000000000000000000
χ694-44-4-44-4400400-400-44000000000000002-22-2-22-22-22-222-22-200000000000000000000000000000000
χ704-44-4-44-4400400-400-4400000000000000-22-222-22-22-22-2-22-2200000000000000000000000000000000
χ714-44-4-44-4400-4004004-4000000000000002-22-22-22-2-22-22-22-2200000000000000000000000000000000
χ724-44-4-44-4400-4004004-400000000000000-22-22-22-222-22-22-22-200000000000000000000000000000000
χ734-4-444i−4i−4i4i4-400004i−4i00000000000000002-2-222i−2i−2i2i2i−2i−2i2i2-2-2200000000000000000000000000000000
χ744-4-444i−4i−4i4i4-400004i−4i0000000000000000-222-2−2i2i2i−2i−2i2i2i−2i-222-200000000000000000000000000000000
χ754-4-444i−4i−4i4i-440000−4i4i00000000000000002-2-22−2i2i2i−2i2i−2i−2i2i-222-200000000000000000000000000000000
χ764-4-444i−4i−4i4i-440000−4i4i0000000000000000-222-22i−2i−2i2i−2i2i2i−2i2-2-2200000000000000000000000000000000
χ774-4-44−4i4i4i−4i4-40000−4i4i00000000000000002-2-22−2i2i2i−2i−2i2i2i−2i2-2-2200000000000000000000000000000000
χ784-4-44−4i4i4i−4i4-40000−4i4i0000000000000000-222-22i−2i−2i2i2i−2i−2i2i-222-200000000000000000000000000000000
χ794-4-44−4i4i4i−4i-4400004i−4i00000000000000002-2-222i−2i−2i2i−2i2i2i−2i-222-200000000000000000000000000000000
χ804-4-44−4i4i4i−4i-4400004i−4i0000000000000000-222-2−2i2i2i−2i2i−2i−2i2i2-2-2200000000000000000000000000000000

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