Finite Group Databasebeta

← Group #153393

Character table — Group #153393

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222222222444444444444444444444488888888888888883232323232323232
order12442224448888161616161616161644448888881616161616161616161616163232323232323232323232323232323244448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ922222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ1022222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222222222000000000000000000000000
χ112222222222-2-2-2-2000000002222-2-2-2-2-2-20000000000002222−2−2−2−22222−2−2−2−200000000
χ122222222222-2-2-2-2000000002222-2-2-2-2-2-2000000000000−2−2−2−22222−2−2−2−2222200000000
χ132222222222-2-2-2-200000000-2-2-2-22222-2-20000000000002222−2−2−2−2−2−2−2−2222200000000
χ142222222222-2-2-2-200000000-2-2-2-22222-2-2000000000000−2−2−2−222222222−2−2−2−200000000
χ1522222-2-2-2-2222222222222200000000-2-2-2-2-2-20000000022-2-222-2-20000000000000000
χ1622222-2-2-2-2222222222222200000000-2-2-2-2-2-200000000-2-222-2-2220000000000000000
χ1722222-2-2-2-222222-2-2-2-2-2-2-2-200000000-2-2222200000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ1822222-2-2-2-222222-2-2-2-2-2-2-2-200000000-2-222220000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ1922222-2-2-2-22-2-2-2-200000000000000002200002i2i2i2i−2i−2i−2i−2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000
χ2022222-2-2-2-22-2-2-2-200000000000000002200002i2i2i2i−2i−2i−2i−2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000
χ2122222-2-2-2-22-2-2-2-20000000000000000220000−2i−2i−2i−2i2i2i2i2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000
χ2222222-2-2-2-22-2-2-2-20000000000000000220000−2i−2i−2i−2i2i2i2i2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000
χ2322-2-2222-2-2-2000022−2−222−2−200002i2i−2i−2i0022−2−2i2i2−i2−i2i2i2−i2−i2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ500000000
χ2422-2-2222-2-2-2000022−2−222−2−200002i2i−2i−2i0022−2−2i2i2−i2−i2i2i2−i2−i2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ500000000
χ2522-2-2222-2-2-2000022−2−222−2−20000−2i−2i2i2i0022−2−2−i2−i2i2i2−i2−i2i2i2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ500000000
χ2622-2-2222-2-2-2000022−2−222−2−20000−2i−2i2i2i0022−2−2−i2−i2i2i2−i2−i2i2i2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ500000000
χ2722-2-2222-2-2-20000−2−222−2−22200002i2i−2i−2i00−2−222−i2−i2i2i2−i2−i2i2i2ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ700000000
χ2822-2-2222-2-2-20000−2−222−2−22200002i2i−2i−2i00−2−222−i2−i2i2i2−i2−i2i2i2−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ700000000
χ2922-2-2222-2-2-20000−2−222−2−2220000−2i−2i2i2i00−2−222i2i2−i2−i2i2i2−i2−i2ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ700000000
χ3022-2-2222-2-2-20000−2−222−2−2220000−2i−2i2i2i00−2−222i2i2−i2−i2i2i2−i2−i2−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ700000000
χ3122-2-22-2-222-2000022−2−222−2−222-2-2000000−2−22222−2−2−2−222ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ500000000
χ3222-2-22-2-222-2000022−2−222−2−222-2-2000000−2−22222−2−2−2−222−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ500000000
χ3322-2-22-2-222-2000022−2−222−2−2-2-222000000−2−222−2−22222−2−2ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ500000000
χ3422-2-22-2-222-2000022−2−222−2−2-2-222000000−2−222−2−22222−2−2−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ500000000
χ3522-2-22-2-222-20000−2−222−2−22222-2-200000022−2−2−2−22222−2−2ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ700000000
χ3622-2-22-2-222-20000−2−222−2−22222-2-200000022−2−2−2−22222−2−2−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ700000000
χ3722-2-22-2-222-20000−2−222−2−222-2-22200000022−2−222−2−2−2−222ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ700000000
χ3822-2-22-2-222-20000−2−222−2−222-2-22200000022−2−222−2−2−2−222−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ700000000
χ3922-2-2-22-22-2222-2-22222-2-2-2-2000000002-22-22-2000000000000000000000000002-20000
χ4022-2-2-22-22-2222-2-22222-2-2-2-2000000002-22-22-200000000000000000000000000-220000
χ4122-2-2-22-22-2222-2-2-2-2-2-22222000000002-2-22-220000000000000000000000000000002i−2i
χ4222-2-2-22-22-2222-2-2-2-2-2-22222000000002-2-22-22000000000000000000000000000000−2i2i
χ4322-2-2-2-22-22222-2-22222-2-2-2-200000000-22-22-220000000000000000000000002-2000000
χ4422-2-2-2-22-22222-2-22222-2-2-2-200000000-22-22-22000000000000000000000000-22000000
χ4522-2-2-2-22-22222-2-2-2-2-2-2222200000000-222-22-200000000000000000000000000002i−2i00
χ4622-2-2-2-22-22222-2-2-2-2-2-2222200000000-222-22-20000000000000000000000000000−2i2i00
χ474444-44-4-44-400002222−22−22−22−222222000000000022−22−222200000000000000000000000000000000
χ484444-44-4-44-40000−22−2222222222−22−220000000000−222222−2200000000000000000000000000000000
χ494444-4-444-4-400002222−22−22−22−2222220000000000−222222−2200000000000000000000000000000000
χ504444-4-444-4-40000−22−2222222222−22−22000000000022−22−222200000000000000000000000000000000
χ5144-4-4-44-44-44-4-4440000000000000000-44000000000000000000000000000000000000
χ5244-4-4-4-44-444-4-44400000000000000004-4000000000000000000000000000000000000
χ534-44i−4i00000022−222i2−2i22ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52-22i−2i2ζ2−2ζ22ζ6−2ζ60000002ζ−2ζ2ζ5−2ζ52ζ3−2ζ32ζ7−2ζ7000000000000000000000000
χ544-44i−4i00000022−222i2−2i22ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5-22−2i2i−2ζ22ζ2−2ζ62ζ6000000−2ζ2ζ−2ζ52ζ5−2ζ32ζ3−2ζ72ζ7000000000000000000000000
χ554-44i−4i00000022−222i2−2i2−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52-22i−2i2ζ2−2ζ22ζ6−2ζ6000000−2ζ2ζ−2ζ52ζ5−2ζ32ζ3−2ζ72ζ7000000000000000000000000
χ564-44i−4i00000022−222i2−2i2−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5-22−2i2i−2ζ22ζ2−2ζ62ζ60000002ζ−2ζ2ζ5−2ζ52ζ3−2ζ32ζ7−2ζ7000000000000000000000000
χ574-44i−4i000000−2222−2i22i22ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72-22i−2i−2ζ22ζ2−2ζ62ζ60000002ζ5−2ζ5−2ζ2ζ−2ζ72ζ72ζ3−2ζ3000000000000000000000000
χ584-44i−4i000000−2222−2i22i22ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7-22−2i2i2ζ2−2ζ22ζ6−2ζ6000000−2ζ52ζ52ζ−2ζ2ζ7−2ζ7−2ζ32ζ3000000000000000000000000
χ594-44i−4i000000−2222−2i22i2−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72-22i−2i−2ζ22ζ2−2ζ62ζ6000000−2ζ52ζ52ζ−2ζ2ζ7−2ζ7−2ζ32ζ3000000000000000000000000
χ604-44i−4i000000−2222−2i22i2−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7-22−2i2i2ζ2−2ζ22ζ6−2ζ60000002ζ5−2ζ5−2ζ2ζ−2ζ72ζ72ζ3−2ζ3000000000000000000000000
χ614-4−4i4i00000022−22−2i22i22ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52-2−2i2i−2ζ62ζ6−2ζ22ζ20000002ζ7−2ζ72ζ3−2ζ32ζ5−2ζ52ζ−2ζ000000000000000000000000
χ624-4−4i4i00000022−22−2i22i22ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5-222i−2i2ζ6−2ζ62ζ2−2ζ2000000−2ζ72ζ7−2ζ32ζ3−2ζ52ζ5−2ζ2ζ000000000000000000000000
χ634-4−4i4i00000022−22−2i22i2−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52-2−2i2i−2ζ62ζ6−2ζ22ζ2000000−2ζ72ζ7−2ζ32ζ3−2ζ52ζ5−2ζ2ζ000000000000000000000000
χ644-4−4i4i00000022−22−2i22i2−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5-222i−2i2ζ6−2ζ62ζ2−2ζ20000002ζ7−2ζ72ζ3−2ζ32ζ5−2ζ52ζ−2ζ000000000000000000000000
χ654-4−4i4i000000−22222i2−2i22ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72-2−2i2i2ζ6−2ζ62ζ2−2ζ20000002ζ3−2ζ3−2ζ72ζ7−2ζ2ζ2ζ5−2ζ5000000000000000000000000
χ664-4−4i4i000000−22222i2−2i22ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7-222i−2i−2ζ62ζ6−2ζ22ζ2000000−2ζ32ζ32ζ7−2ζ72ζ−2ζ−2ζ52ζ5000000000000000000000000
χ674-4−4i4i000000−22222i2−2i2−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72-2−2i2i2ζ6−2ζ62ζ2−2ζ2000000−2ζ32ζ32ζ7−2ζ72ζ−2ζ−2ζ52ζ5000000000000000000000000
χ684-4−4i4i000000−22222i2−2i2−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7-222i−2i−2ζ62ζ6−2ζ22ζ20000002ζ3−2ζ3−2ζ72ζ7−2ζ2ζ2ζ5−2ζ5000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.