Finite Group Databasebeta

← Group #111513

Character table — Group #111513

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444444444444444888888888888888844444444888888882222444488888888
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
χ91-1-111-1-1111-1-1111-1-11111-1-1-1-11-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1111-1-1-1-11-11-11-11-1ii−i−iii−i−i
χ101-1-111-1-1111-1-1111-1-11111-1-1-1-11-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-11-11-11-11−i−iii−i−iii
χ111-1-111-1-1111-1-1111-1-11111-1-1-1-11-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1-1-111111-1-111-1-11ii−i−i−i−iii
χ121-1-111-1-1111-1-1111-1-11111-1-1-1-11-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1-1-11111-111-1-111-1−i−iiiii−i−i
χ131-1-111-1-1111-1-1111-1-11111-1-1-1-11-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-1-1-111111-1-111-1-11−i−iiiii−i−i
χ141-1-111-1-1111-1-1111-1-11111-1-1-1-11-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-1-1-11111-111-1-111-1ii−i−i−i−iii
χ151-1-111-1-1111-1-1111-1-11111-1-1-1-11-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1111-1-1-1-11-11-11-11-1−i−iii−i−iii
χ161-1-111-1-1111-1-1111-1-11111-1-1-1-11-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1111-1-1-1-1-11-11-11-11ii−i−iii−i−i
χ1722222222222222222-2-2-2-2-2-2222-2-2-2-2-2-200000000000000000000000022-2-222-2-20000000000000000
χ1822222222222222222-2-2-2-2-2-2222-2-2-2-2-2-2000000000000000000000000-2-222-2-2220000000000000000
χ19222222222222-2-2-2-2-2222222-2-2-222-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ20222222222222-2-2-2-2-2222222-2-2-222-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ2322222222-2-2-2-222-2-2-222-2-22-222-22-22-22-2000000000000000000000000000000000000000000002-22-2
χ2422222222-2-2-2-222-2-2-222-2-22-222-22-22-22-200000000000000000000000000000000000000000000-22-22
χ2522222222-2-2-2-222-2-2-2-2-222-2222-2-22-22-2200000000000000000000000000000000000000002-22-20000
χ2622222222-2-2-2-222-2-2-2-2-222-2222-2-22-22-220000000000000000000000000000000000000000-22-220000
χ2722222222-2-2-2-2-2-222222-2-22-2-2-222-2-22-22000000000000000000000000000000002200-2-20000000000
χ2822222222-2-2-2-2-2-222222-2-22-2-2-222-2-22-2200000000000000000000000000000000-2-200220000000000
χ2922222222-2-2-2-2-2-2222-2-222-22-2-22-222-22-200000000000000000000000000000000002200-2-200000000
χ3022222222-2-2-2-2-2-2222-2-222-22-2-22-222-22-20000000000000000000000000000000000-2-2002200000000
χ3122-2-2-22-222-22-2000002-22-222000-2-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002i−2i002i−2i2−22−22−22−20000000000000000
χ3222-2-2-22-222-22-2000002-22-222000-2-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200−2i2i00−2i2i−22−22−22−220000000000000000
χ3322-2-2-22-222-22-2000002-22-222000-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002i−2i002i−2i−22−22−22−220000000000000000
χ3422-2-2-22-222-22-2000002-22-222000-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200−2i2i00−2i2i2−22−22−22−20000000000000000
χ3522-2-2-22-222-22-200000-22-22-2-200022000022−2−2−2−22222−2−2−2−2222-2002-2002−2−222−2−220000000000000000
χ3622-2-2-22-222-22-200000-22-22-2-200022000022−2−2−2−22222−2−2−2−222-2200-2200−222−2−222−20000000000000000
χ3722-2-2-22-222-22-200000-22-22-2-2000220000−2−22222−2−2−2−22222−2−22-2002-200−222−2−222−20000000000000000
χ3822-2-2-22-222-22-200000-22-22-2-2000220000−2−22222−2−2−2−22222−2−2-2200-22002−2−222−2−220000000000000000
χ392-22-2-2-2222-2-22000002-22-2-2-200022000022−2−222−2−2−2−222−2−222002-200-222−22−2−22−220000000000000000
χ402-22-2-2-2222-2-22000002-22-2-2-200022000022−2−222−2−2−2−222−2−22200-22002-2−22−222−22−20000000000000000
χ412-22-2-2-2222-2-22000002-22-2-2-2000220000−2−222−2−22222−2−222−2−2002-200-22−22−222−22−20000000000000000
χ422-22-2-2-2222-2-22000002-22-2-2-2000220000−2−222−2−22222−2−222−2−200-22002-22−22−2−22−220000000000000000
χ432-22-2-2-2222-2-2200000-22-2222000-2-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i22i−2i00−2i2i002−2−22−222−20000000000000000
χ442-22-2-2-2222-2-2200000-22-2222000-2-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−2i2i002i−2i00−222−22−2−220000000000000000
χ452-22-2-2-2222-2-2200000-22-2222000-2-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i22i−2i00−2i2i00−222−22−2−220000000000000000
χ462-22-2-2-2222-2-2200000-22-2222000-2-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−2i2i002i−2i002−2−22−222−20000000000000000
χ472-2-222-2-2222-2-2222-2-2-2-2-2-222-2-2222-2-22200000000000000000000000022-2-2-2-2220000000000000000
χ482-2-222-2-2222-2-2222-2-2-2-2-2-222-2-2222-2-222000000000000000000000000-2-22222-2-20000000000000000
χ492-2-222-2-2222-2-2-2-2-2222222-2-222-2-2-2-2-22200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ502-2-222-2-2222-2-2-2-2-2222222-2-222-2-2-2-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ512-2-222-2-2222-2-2-2-2-222-2-2-2-22222-22222-2-22222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ522-2-222-2-2222-2-2-2-2-222-2-2-2-22222-22222-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ532-2-222-2-22-2-22222-22222-2-2-22-2-2-2-222-2-22000000000000000000000000000000000000000000002i−2i−2i2i
χ542-2-222-2-22-2-22222-22222-2-2-22-2-2-2-222-2-2200000000000000000000000000000000000000000000−2i2i2i−2i
χ552-2-222-2-22-2-22222-222-2-2222-2-2-2-22-2-222-200000000000000000000000000000000000000002i−2i−2i2i0000
χ562-2-222-2-22-2-22222-222-2-2222-2-2-2-22-2-222-20000000000000000000000000000000000000000−2i2i2i−2i0000
χ572-2-222-2-22-2-222-2-22-2-222-2-2-22222-22-222-2000000000000000000000000000000002-200-220000000000
χ582-2-222-2-22-2-222-2-22-2-222-2-2-22222-22-222-200000000000000000000000000000000-22002-20000000000
χ592-2-222-2-22-2-222-2-22-2-2-2-2222-22222-22-2-2200000000000000000000000000000000002-200-2200000000
χ602-2-222-2-22-2-222-2-22-2-2-2-2222-22222-22-2-220000000000000000000000000000000000-22002-200000000
χ614444-4-4-4-400000044-400000000-40000002-22-22-22-22-22-22-22-200000000000000000000000000000000
χ624444-4-4-4-400000044-400000000-4000000-22-22-22-22-22-22-22-2200000000000000000000000000000000
χ634444-4-4-4-4000000-4-440000000040000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ644444-4-4-4-4000000-4-44000000004000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ6544-4-44-44-400004i−4i0000000004i−4i00000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000000000000000
χ6644-4-44-44-400004i−4i0000000004i−4i0000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000000000000000
χ6744-4-44-44-40000−4i4i000000000−4i4i00000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000000000000000000000
χ6844-4-44-44-40000−4i4i000000000−4i4i0000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000000000000000000000
χ6944-4-4-44-44-44-44000004-4-444-4000-440000000000000000000000000000000000000000000000000000
χ7044-4-4-44-44-44-4400000-444-4-440004-40000000000000000000000000000000000000000000000000000
χ714-44-444-4-400004i−4i000000000−4i4i00000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000000000000000000000000000
χ724-44-444-4-400004i−4i000000000−4i4i0000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000000000000000000000000000
χ734-44-444-4-40000−4i4i0000000004i−4i00000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000000000000000
χ744-44-444-4-40000−4i4i0000000004i−4i0000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000000000000000
χ754-44-4-4-444-444-4000004-4-44-440004-40000000000000000000000000000000000000000000000000000
χ764-44-4-4-444-444-400000-444-44-4000-440000000000000000000000000000000000000000000000000000
χ774-4-44-444-40000004-4400000000-40000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ784-4-44-444-40000004-4400000000-4000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ794-4-44-444-4000000-44-40000000040000002-22-2-22-22-22-222-22-200000000000000000000000000000000
χ804-4-44-444-4000000-44-4000000004000000-22-222-22-22-22-2-22-2200000000000000000000000000000000

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