Finite Group Databasebeta

← Group #121582

Character table — Group #121582

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444444444444444888888888888888844444444888888884444444488888888
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
χ91-1111-1-1-111-1-111111-1-1-1-1-1-1-1-111111-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−iii−i−i1111-1-1-1-1i−ii−ii−ii−i11-1-111-1-1
χ101-1111-1-1-111-1-111111-1-1-1-1-1-1-1-111111-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−iii−i−i1111-1-1-1-1−ii−ii−ii−ii-1-111-1-111
χ111-1111-1-1-111-1-111111-1-1-1-1-1-1-1-111111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−iii-1-1-1-11111i−i−iii−i−ii11-1-1-1-111
χ121-1111-1-1-111-1-111111-1-1-1-1-1-1-1-111111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−iii-1-1-1-11111−iii−i−iii−i-1-11111-1-1
χ131-1111-1-1-111-1-111111-1-1-1-1-1-1-1-111111-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−iii−i−i-1-1-1-11111i−i−iii−i−ii-1-11111-1-1
χ141-1111-1-1-111-1-111111-1-1-1-1-1-1-1-111111-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−iii−i−i-1-1-1-11111−iii−i−iii−i11-1-1-1-111
χ151-1111-1-1-111-1-111111-1-1-1-1-1-1-1-111111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−iii1111-1-1-1-1i−ii−ii−ii−i-1-111-1-111
χ161-1111-1-1-111-1-111111-1-1-1-1-1-1-1-111111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−iii1111-1-1-1-1−ii−ii−ii−ii11-1-111-1-1
χ17222222222222222-2-222-2-2-2-2222-2-2-2-2-2-200000000000000000000000022-2-222-2-20000000000000000
χ18222222222222222-2-222-2-2-2-2222-2-2-2-2-2-2000000000000000000000000-2-222-2-2220000000000000000
χ19222222222222-2-2-222-2-22222-2-2-222-2-2-2-200000000000000002222-2-2-2-2000000000000000000000000
χ20222222222222-2-2-222-2-22222-2-2-222-2-2-2-20000000000000000-2-2-2-22222000000000000000000000000
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
χ2322222222-2-2-2-222-22-2-2-222-2-222-22-22-22-2000000000000000000000000000000000000000000002-22-2
χ2422222222-2-2-2-222-22-2-2-222-2-222-22-22-22-200000000000000000000000000000000000000000000-22-22
χ2522222222-2-2-2-222-2-22-2-2-2-22222-2-22-22-2200000000000000000000000000000000000000002-22-20000
χ2622222222-2-2-2-222-2-22-2-2-2-22222-2-22-22-220000000000000000000000000000000000000000-22-220000
χ2722222222-2-2-2-2-2-222-22222-2-2-2-222-2-22-22000000000000000000000000000000002200-2-20000000000
χ2822222222-2-2-2-2-2-222-22222-2-2-2-222-2-22-2200000000000000000000000000000000-2-200220000000000
χ2922222222-2-2-2-2-2-22-2222-2-222-2-22-222-22-200000000000000000000000000000000002200-2-200000000
χ3022222222-2-2-2-2-2-22-2222-2-222-2-22-222-22-20000000000000000000000000000000000-2-2002200000000
χ31222-2-22-2-22-22-200022002-22-2000-2-2000022−2−222−2−222−2−222−2−22-22-200002−22−22−22−20000000000000000
χ32222-2-22-2-22-22-200022002-22-2000-2-2000022−2−222−2−222−2−222−2−2-22-220000−22−22−22−220000000000000000
χ33222-2-22-2-22-22-200022002-22-2000-2-20000−2−222−2−222−2−222−2−2222-22-20000−22−22−22−220000000000000000
χ34222-2-22-2-22-22-200022002-22-2000-2-20000−2−222−2−222−2−222−2−222-22-2200002−22−22−22−20000000000000000
χ35222-2-22-2-22-22-2000-2-200-22-22000220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200002i−2i2i−2i2−2−222−2−220000000000000000
χ36222-2-22-2-22-22-2000-2-200-22-22000220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000−2i2i−2i2i−222−2−222−20000000000000000
χ37222-2-22-2-22-22-2000-2-200-22-22000220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200002i−2i2i−2i−222−2−222−20000000000000000
χ38222-2-22-2-22-22-2000-2-200-22-22000220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000−2i2i−2i2i2−2−222−2−220000000000000000
χ392-2222-2-2-222-2-2222-2-2-2-22222-2-22-2-2-2-22200000000000000000000000022-2-2-2-2220000000000000000
χ402-2222-2-2-222-2-2222-2-2-2-22222-2-22-2-2-2-222000000000000000000000000-2-22222-2-20000000000000000
χ412-2222-2-2-222-2-2-2-2-22222-2-2-2-222-222-2-22200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ422-2222-2-2-222-2-2-2-2-22222-2-2-2-222-222-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ432-2222-2-2-222-2-2-2-2-2-2-222222222-2-2-222-2-22222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ442-2222-2-2-222-2-2-2-2-2-2-222222222-2-2-222-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ452-2222-2-2-2-2-22222-22-222-2-222-2-2-22-22-2-22000000000000000000000000000000000000000000002-2-22
χ462-2222-2-2-2-2-22222-22-222-2-222-2-2-22-22-2-2200000000000000000000000000000000000000000000-222-2
χ472-2222-2-2-2-2-22222-2-222222-2-2-2-2-2-22-222-200000000000000000000000000000000000000002-2-220000
χ482-2222-2-2-2-2-22222-2-222222-2-2-2-2-2-22-222-20000000000000000000000000000000000000000-222-20000
χ492-2222-2-2-2-2-222-2-222-2-2-2-2-2222222-2-222-2000000000000000000000000000000002i−2i00−2i2i0000000000
χ502-2222-2-2-2-2-222-2-222-2-2-2-2-2222222-2-222-200000000000000000000000000000000−2i2i002i−2i0000000000
χ512-2222-2-2-2-2-222-2-22-22-2-222-2-2222-222-2-2200000000000000000000000000000000002i−2i00−2i2i00000000
χ522-2222-2-2-2-2-222-2-22-22-2-222-2-2222-222-2-220000000000000000000000000000000000−2i2i002i−2i00000000
χ532-22-2-2-2222-2-220002200-22-22000-2-20000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i22i−2i−2i2i00002−22−2−22−220000000000000000
χ542-22-2-2-2222-2-220002200-22-22000-2-20000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−2i2i2i−2i0000−22−222−22−20000000000000000
χ552-22-2-2-2222-2-220002200-22-22000-2-20000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i22i−2i−2i2i0000−22−222−22−20000000000000000
χ562-22-2-2-2222-2-220002200-22-22000-2-20000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−2i2i2i−2i00002−22−2−22−220000000000000000
χ572-22-2-2-2222-2-22000-2-2002-22-200022000022−2−2−2−222−2−22222−2−200002-2-222−2−22−222−20000000000000000
χ582-22-2-2-2222-2-22000-2-2002-22-200022000022−2−2−2−222−2−22222−2−20000-222-2−222−22−2−220000000000000000
χ592-22-2-2-2222-2-22000-2-2002-22-2000220000−2−22222−2−222−2−2−2−22200002-2-22−222−22−2−220000000000000000
χ602-22-2-2-2222-2-22000-2-2002-22-2000220000−2−22222−2−222−2−2−2−2220000-222-22−2−22−222−20000000000000000
χ61444-4-44-4-4-44-440004-4004-4-44000-440000000000000000000000000000000000000000000000000000
χ62444-4-44-4-4-44-44000-4400-444-40004-40000000000000000000000000000000000000000000000000000
χ6344-44-4-44-40000004004-4000000-40000002-22-22-22-22-22-22-22-200000000000000000000000000000000
χ6444-44-4-44-40000004004-4000000-4000000-22-22-22-22-22-22-22-2200000000000000000000000000000000
χ6544-44-4-44-4000000-400-4400000040000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ6644-44-4-44-4000000-400-440000004000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ6744-4-44-4-4400004i−4i0000000004i−4i00000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000000000000000
χ6844-4-44-4-4400004i−4i0000000004i−4i0000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000000000000000
χ6944-4-44-4-440000−4i4i000000000−4i4i00000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000000000000000000000000000
χ7044-4-44-4-440000−4i4i000000000−4i4i0000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000000000000000000000000000
χ714-44-4-4-444-444-40004-400-444-4000-440000000000000000000000000000000000000000000000000000
χ724-44-4-4-444-444-4000-44004-4-440004-40000000000000000000000000000000000000000000000000000
χ734-4-44-44-44000000400-44000000-40000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ744-4-44-44-44000000400-44000000-4000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ754-4-44-44-44000000-4004-400000040000002-22-2-22-22-22-222-22-200000000000000000000000000000000
χ764-4-44-44-44000000-4004-40000004000000-22-222-22-22-22-2-22-2200000000000000000000000000000000
χ774-4-4-4444-400004i−4i000000000−4i4i00000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000000000000000000000
χ784-4-4-4444-400004i−4i000000000−4i4i0000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000000000000000000000
χ794-4-4-4444-40000−4i4i0000000004i−4i00000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000000000000000
χ804-4-4-4444-40000−4i4i0000000004i−4i0000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000000000000000

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