Finite Group Databasebeta

← Group #140372

Character table — Group #140372

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12448888222444444488888888884488888888888888888816161616161616161616161616161616444488881616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ91111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111iiiiiiii−i−i−i−i−i−i−i−iii−i−iii−i−i1111-1-1-1-11111-1-1-1-1ii−i−iii−i−i
χ101111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111iiiiiiii−i−i−i−i−i−i−i−iii−i−iii−i−i1111-1-1-1-1-1-1-1-11111−i−iii−i−iii
χ111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−iii-1-1-1-1111111-1-1-1-111ii−i−i−i−iii
χ121111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−iii-1-1-1-11111-1-11111-1-1−i−iiiii−i−i
χ131111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111−i−i−i−i−i−i−i−iiiiiiiiiii−i−iii−i−i-1-1-1-1111111-1-1-1-111−i−iiiii−i−i
χ141111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111−i−i−i−i−i−i−i−iiiiiiiiiii−i−iii−i−i-1-1-1-11111-1-11111-1-1ii−i−i−i−iii
χ151111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−iii−i−iii
χ161111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−iii1111-1-1-1-1-1-1-1-11111ii−i−iii−i−i
χ17222222222222-2-2-2-222222222-2-2-2-2-2-2-2-200000000000000002222-2-2-2-2000000000000000000000000
χ18222222222222-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-22222000000000000000000000000
χ19222222222-2-222222-2-2-2-2-2-2222222-2-2-2-200000000000000000000000022-2-222-2-20000000000000000
χ20222222222-2-222222-2-2-2-2-2-2222222-2-2-2-2000000000000000000000000-2-222-2-2220000000000000000
χ21222222222-2-22-2-2-2-2-2-2-2-2-2-222-2-2-2-222222i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ22222222222-2-22-2-2-2-2-2-2-2-2-2-222-2-2-2-22222−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ232222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-222-2-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ242222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ252222-2-2-2-22-2-222222-2-22222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ262222-2-2-2-22-2-222222-2-22222-2-2-2-2-2-2-2-222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ272222-2-2-2-22-2-22-2-2-2-2-2-22222-2-2222222-2-200000000000000000000000022-2-2-2-2220000000000000000
χ282222-2-2-2-22-2-22-2-2-2-2-2-22222-2-2222222-2-2000000000000000000000000-2-22222-2-20000000000000000
χ2922-2-22i2i−2i−2i222-20000-2-22i2i−2i−2i2i−2i000000001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i00002ζ−2ζ2ζ3−2ζ32−22−2i2−i2i2−i20000000000000000
χ3022-2-22i2i−2i−2i222-20000-2-22i2i−2i−2i2i−2i000000001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i0000−2ζ2ζ−2ζ32ζ3−22−22−i2i2−i2i20000000000000000
χ3122-2-22i2i−2i−2i222-20000-2-22i2i−2i−2i2i−2i00000000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i00002ζ−2ζ2ζ3−2ζ3−22−22−i2i2−i2i20000000000000000
χ3222-2-22i2i−2i−2i222-20000-2-22i2i−2i−2i2i−2i00000000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i0000−2ζ2ζ−2ζ32ζ32−22−2i2−i2i2−i20000000000000000
χ3322-2-22i2i−2i−2i2-2-2-2000022−2i−2i2i2i2i−2i000000001−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i2ζ3−2ζ32ζ−2ζ00002−2−22i2−i2−i2i20000000000000000
χ3422-2-22i2i−2i−2i2-2-2-2000022−2i−2i2i2i2i−2i000000001−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−2ζ32ζ3−2ζ2ζ0000−222−2−i2i2i2−i20000000000000000
χ3522-2-22i2i−2i−2i2-2-2-2000022−2i−2i2i2i2i−2i00000000−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i2ζ3−2ζ32ζ−2ζ0000−222−2−i2i2i2−i20000000000000000
χ3622-2-22i2i−2i−2i2-2-2-2000022−2i−2i2i2i2i−2i00000000−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−2ζ32ζ3−2ζ2ζ00002−2−22i2−i2−i2i20000000000000000
χ3722-2-22i2i−2i−2i-22-222i2i−2i−2i2-22i−2i2i−2i−2i2i22-2-22i−2i2-200000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ3822-2-22i2i−2i−2i-22-222i2i−2i−2i2-22i−2i2i−2i−2i2i22-2-22i−2i2-20000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ3922-2-22i2i−2i−2i-22-22−2i−2i2i2i2-22i−2i2i−2i−2i2i-2-222−2i2i-2200000000000000000000000000000000002i−2i002-200000000
χ4022-2-22i2i−2i−2i-22-22−2i−2i2i2i2-22i−2i2i−2i−2i2i-2-222−2i2i-220000000000000000000000000000000000−2i2i00-2200000000
χ4122-2-22i2i−2i−2i-2-2222i2i−2i−2i-22−2i2i−2i2i−2i2i22-2-2−2i2i-22000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ4222-2-22i2i−2i−2i-2-2222i2i−2i−2i-22−2i2i−2i2i−2i2i22-2-2−2i2i-2200000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ4322-2-22i2i−2i−2i-2-222−2i−2i2i2i-22−2i2i−2i2i−2i2i-2-2222i−2i2-2000000000000000000000000000000002i−2i002-20000000000
χ4422-2-22i2i−2i−2i-2-222−2i−2i2i2i-22−2i2i−2i2i−2i2i-2-2222i−2i2-200000000000000000000000000000000−2i2i00-220000000000
χ4522-2-2−2i−2i2i2i222-20000-2-2−2i−2i2i2i−2i2i000000001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i00002ζ3−2ζ32ζ−2ζ−22−22i2−i2i2−i20000000000000000
χ4622-2-2−2i−2i2i2i222-20000-2-2−2i−2i2i2i−2i2i000000001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i0000−2ζ32ζ3−2ζ2ζ2−22−2−i2i2−i2i20000000000000000
χ4722-2-2−2i−2i2i2i222-20000-2-2−2i−2i2i2i−2i2i00000000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i00002ζ3−2ζ32ζ−2ζ2−22−2−i2i2−i2i20000000000000000
χ4822-2-2−2i−2i2i2i222-20000-2-2−2i−2i2i2i−2i2i00000000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i0000−2ζ32ζ3−2ζ2ζ−22−22i2−i2i2−i20000000000000000
χ4922-2-2−2i−2i2i2i2-2-2-20000222i2i−2i−2i−2i2i000000001+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i2ζ−2ζ2ζ3−2ζ30000−222−2i2−i2−i2i20000000000000000
χ5022-2-2−2i−2i2i2i2-2-2-20000222i2i−2i−2i−2i2i000000001+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−2ζ2ζ−2ζ32ζ300002−2−22−i2i2i2−i20000000000000000
χ5122-2-2−2i−2i2i2i2-2-2-20000222i2i−2i−2i−2i2i00000000−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i2ζ−2ζ2ζ3−2ζ300002−2−22−i2i2i2−i20000000000000000
χ5222-2-2−2i−2i2i2i2-2-2-20000222i2i−2i−2i−2i2i00000000−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−2ζ2ζ−2ζ32ζ30000−222−2i2−i2−i2i20000000000000000
χ5322-2-2−2i−2i2i2i-22-222i2i−2i−2i2-2−2i2i−2i2i2i−2i-2-2222i−2i-2200000000000000000000000000000000002i−2i00-2200000000
χ5422-2-2−2i−2i2i2i-22-222i2i−2i−2i2-2−2i2i−2i2i2i−2i-2-2222i−2i-220000000000000000000000000000000000−2i2i002-200000000
χ5522-2-2−2i−2i2i2i-22-22−2i−2i2i2i2-2−2i2i−2i2i2i−2i22-2-2−2i2i2-200000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ5622-2-2−2i−2i2i2i-22-22−2i−2i2i2i2-2−2i2i−2i2i2i−2i22-2-2−2i2i2-20000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ5722-2-2−2i−2i2i2i-2-2222i2i−2i−2i-222i−2i2i−2i2i−2i-2-222−2i2i2-2000000000000000000000000000000002i−2i00-220000000000
χ5822-2-2−2i−2i2i2i-2-2222i2i−2i−2i-222i−2i2i−2i2i−2i-2-222−2i2i2-200000000000000000000000000000000−2i2i002-20000000000
χ5922-2-2−2i−2i2i2i-2-222−2i−2i2i2i-222i−2i2i−2i2i−2i22-2-22i−2i-22000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ6022-2-2−2i−2i2i2i-2-222−2i−2i2i2i-222i−2i2i−2i2i−2i22-2-22i−2i-2200000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ6144444444-44-4-40000-444-4-44-4-400000000000000000000000000000000000000000000000000000000
χ6244444444-4-44-400004-4-444-4-4-400000000000000000000000000000000000000000000000000000000
χ634444-4-4-4-4-44-4-40000-44-444-44400000000000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-4-44-400004-44-4-444400000000000000000000000000000000000000000000000000000000
χ654-44i−4i4ζ−4ζ4ζ3−4ζ300002+2i−2−2i2−2i−2+2i0000000022−222i2−2i200002-22i−2i2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2-22i−2i00000000000000000000000000000000
χ664-44i−4i4ζ−4ζ4ζ3−4ζ300002+2i−2−2i2−2i−2+2i0000000022−222i2−2i20000-22−2i2i−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ-22−2i2i00000000000000000000000000000000
χ674-44i−4i4ζ−4ζ4ζ3−4ζ30000−2−2i2+2i−2+2i2−2i00000000−2222−2i22i200002i−2i-22−2ζ32ζ32ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2i2i2-200000000000000000000000000000000
χ684-44i−4i4ζ−4ζ4ζ3−4ζ30000−2−2i2+2i−2+2i2−2i00000000−2222−2i22i20000−2i2i2-22ζ3−2ζ3−2ζ2ζ2ζ−2ζ−2ζ32ζ32i−2i-2200000000000000000000000000000000
χ694-44i−4i−4ζ4ζ−4ζ34ζ300002+2i−2−2i2−2i−2+2i00000000−2222−2i22i200002-22i−2i−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ2-22i−2i00000000000000000000000000000000
χ704-44i−4i−4ζ4ζ−4ζ34ζ300002+2i−2−2i2−2i−2+2i00000000−2222−2i22i20000-22−2i2i2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ-22−2i2i00000000000000000000000000000000
χ714-44i−4i−4ζ4ζ−4ζ34ζ30000−2−2i2+2i−2+2i2−2i0000000022−222i2−2i200002i−2i-222ζ3−2ζ3−2ζ2ζ2ζ−2ζ−2ζ32ζ3−2i2i2-200000000000000000000000000000000
χ724-44i−4i−4ζ4ζ−4ζ34ζ30000−2−2i2+2i−2+2i2−2i0000000022−222i2−2i20000−2i2i2-2−2ζ32ζ32ζ−2ζ−2ζ2ζ2ζ3−2ζ32i−2i-2200000000000000000000000000000000
χ734-4−4i4i4ζ3−4ζ34ζ−4ζ00002−2i−2+2i2+2i−2−2i00000000−22222i2−2i200002-2−2i2i2ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ32-2−2i2i00000000000000000000000000000000
χ744-4−4i4i4ζ3−4ζ34ζ−4ζ00002−2i−2+2i2+2i−2−2i00000000−22222i2−2i20000-222i−2i−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3-222i−2i00000000000000000000000000000000
χ754-4−4i4i4ζ3−4ζ34ζ−4ζ0000−2+2i2−2i−2−2i2+2i0000000022−22−2i22i200002i−2i2-22ζ−2ζ−2ζ32ζ32ζ3−2ζ3−2ζ2ζ−2i2i-2200000000000000000000000000000000
χ764-4−4i4i4ζ3−4ζ34ζ−4ζ0000−2+2i2−2i−2−2i2+2i0000000022−22−2i22i20000−2i2i-22−2ζ2ζ2ζ3−2ζ3−2ζ32ζ32ζ−2ζ2i−2i2-200000000000000000000000000000000
χ774-4−4i4i−4ζ34ζ3−4ζ4ζ00002−2i−2+2i2+2i−2−2i0000000022−22−2i22i200002-2−2i2i−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ32-2−2i2i00000000000000000000000000000000
χ784-4−4i4i−4ζ34ζ3−4ζ4ζ00002−2i−2+2i2+2i−2−2i0000000022−22−2i22i20000-222i−2i2ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ3-222i−2i00000000000000000000000000000000
χ794-4−4i4i−4ζ34ζ3−4ζ4ζ0000−2+2i2−2i−2−2i2+2i00000000−22222i2−2i200002i−2i2-2−2ζ2ζ2ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2i2i-2200000000000000000000000000000000
χ804-4−4i4i−4ζ34ζ3−4ζ4ζ0000−2+2i2−2i−2−2i2+2i00000000−22222i2−2i20000−2i2i-222ζ−2ζ−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2i−2i2-200000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.