Finite Group Databasebeta

← Group #506330

Character table — Group #506330

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222224444444444444444444444444488888888888888161616161616161632323232
order124422244488881616161616161616444488888888881616161616161616161616164444881616161616161616224488884488
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11-11-1
χ4111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-11-11
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-11-111-1-1-11-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11-1-1111-11-1
χ911111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-11-1-1-111-111-1
χ1011111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1111-1-11-1-11
χ1111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ1211111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ1311111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111-11-1-1-1111-1-11
χ1411111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-11-1111-1-1-111-1
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111111111-1-1-1-11111-1-1-1-111-1-1
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-11111-1-111
χ172222222222-2-2-2-2000000002222-2-2-2-22222-2-2000000000000-2-2-2-22200000000000000000000
χ182222222222-2-2-2-2000000002222-2-2-2-2-2-2-2-2-2-20000000000002222-2-200000000000000000000
χ192222222222-2-2-2-200000000-2-2-2-222222222-2-2000000000000-2-222-2-200000000000000000000
χ202222222222-2-2-2-200000000-2-2-2-22222-2-2-2-2-2-200000000000022-2-22200000000000000000000
χ212222-2-222-2-22222222222220000000022-2-2-2-2-2-2-2-2000000002-2000022-2-20000000000000000
χ222222-2-222-2-222222222222200000000-2-222-2-2-2-2-2-200000000-220000-2-2220000000000000000
χ232222-2-222-2-22222-2-2-2-2-2-2-2-20000000022-2-2-2-22222000000002-20000-2-2220000000000000000
χ242222-2-222-2-22222-2-2-2-2-2-2-2-200000000-2-222-2-2222200000000-22000022-2-20000000000000000
χ252222-2-222-2-2-2-2-2-2000000000000000022-2-22200002i2i2i2i−2i−2i−2i−2i-22000000002i2i−2i−2i000000000000
χ262222-2-222-2-2-2-2-2-2000000000000000022-2-2220000−2i−2i−2i−2i2i2i2i2i-2200000000−2i−2i2i2i000000000000
χ272222-2-222-2-2-2-2-2-20000000000000000-2-2222200002i2i2i2i−2i−2i−2i−2i2-200000000−2i−2i2i2i000000000000
χ282222-2-222-2-2-2-2-2-20000000000000000-2-222220000−2i−2i−2i−2i2i2i2i2i2-2000000002i2i−2i−2i000000000000
χ2922-2-2222-2-2-20000i2i2i2i2−i2−i2−i2−i200002i2i−2i−2i2i−2i2i−2i00i2i2−i2−i222−2−222−2−2002-2002−22−2i2−i2i2−i2000000000000
χ3022-2-2222-2-2-20000i2i2i2i2−i2−i2−i2−i200002i2i−2i−2i−2i2i−2i2i00i2i2−i2−i222−2−222−2−200-2200−22−22−i2i2−i2i2000000000000
χ3122-2-2222-2-2-20000i2i2i2i2−i2−i2−i2−i20000−2i−2i2i2i2i−2i2i−2i00i2i2−i2−i2−2−222−2−22200-22002−22−2−i2i2−i2i2000000000000
χ3222-2-2222-2-2-20000i2i2i2i2−i2−i2−i2−i20000−2i−2i2i2i−2i2i−2i2i00i2i2−i2−i2−2−222−2−222002-200−22−22i2−i2i2−i2000000000000
χ3322-2-2222-2-2-20000−i2−i2−i2−i2i2i2i2i200002i2i−2i−2i2i−2i2i−2i00−i2−i2i2i2−2−222−2−222002-200−22−22−i2i2−i2i2000000000000
χ3422-2-2222-2-2-20000−i2−i2−i2−i2i2i2i2i200002i2i−2i−2i−2i2i−2i2i00−i2−i2i2i2−2−222−2−22200-22002−22−2i2−i2i2−i2000000000000
χ3522-2-2222-2-2-20000−i2−i2−i2−i2i2i2i2i20000−2i−2i2i2i2i−2i2i−2i00−i2−i2i2i222−2−222−2−200-2200−22−22i2−i2i2−i2000000000000
χ3622-2-2222-2-2-20000−i2−i2−i2−i2i2i2i2i20000−2i−2i2i2i−2i2i−2i2i00−i2−i2i2i222−2−222−2−2002-2002−22−2−i2i2−i2i2000000000000
χ3722-2-22-2-222-2-2-2222i2i−2i−2i2i2i−2i−2i0000000000002-22i−2i2i−2i0000000000000000000000020-2002i−2i0000
χ3822-2-22-2-222-2-2-2222i2i−2i−2i2i2i−2i−2i0000000000002-22i−2i2i−2i00000000000000000000000-20200−2i2i0000
χ3922-2-22-2-222-2-2-222−2i−2i2i2i−2i−2i2i2i0000000000002-2−2i2i−2i2i0000000000000000000000020-200−2i2i0000
χ4022-2-22-2-222-2-2-222−2i−2i2i2i−2i−2i2i2i0000000000002-2−2i2i−2i2i00000000000000000000000-202002i−2i0000
χ4122-2-2-22-22-22-2-2222i2i−2i−2i2i2i−2i−2i000000000000-22−2i2i−2i2i000000000000000000000020-202i−2i000000
χ4222-2-2-22-22-22-2-2222i2i−2i−2i2i2i−2i−2i000000000000-22−2i2i−2i2i0000000000000000000000-2020−2i2i000000
χ4322-2-2-22-22-22-2-222−2i−2i2i2i−2i−2i2i2i000000000000-222i−2i2i−2i000000000000000000000020-20−2i2i000000
χ4422-2-2-22-22-22-2-222−2i−2i2i2i−2i−2i2i2i000000000000-222i−2i2i−2i0000000000000000000000-20202i−2i000000
χ4522-2-2-2-22-2220000i2i2i2i2−i2−i2−i2−i222-2-200002i−2i−2i2i00−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200002i−2i2−2−22−222−2000000000000
χ4622-2-2-2-22-2220000i2i2i2i2−i2−i2−i2−i222-2-20000−2i2i2i−2i00−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000−2i2i−222−22−2−22000000000000
χ4722-2-2-2-22-2220000i2i2i2i2−i2−i2−i2−i2-2-22200002i−2i−2i2i00−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000−2i2i2−2−222−2−22000000000000
χ4822-2-2-2-22-2220000i2i2i2i2−i2−i2−i2−i2-2-2220000−2i2i2i−2i00−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200002i−2i−222−2−222−2000000000000
χ4922-2-2-2-22-2220000−i2−i2−i2−i2i2i2i2i222-2-200002i−2i−2i2i00i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200002i−2i−222−22−2−22000000000000
χ5022-2-2-2-22-2220000−i2−i2−i2−i2i2i2i2i222-2-20000−2i2i2i−2i00i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000−2i2i2−2−22−222−2000000000000
χ5122-2-2-2-22-2220000−i2−i2−i2−i2i2i2i2i2-2-22200002i−2i−2i2i00i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000−2i2i−222−2−222−2000000000000
χ5222-2-2-2-22-2220000−i2−i2−i2−i2i2i2i2i2-2-2220000−2i2i2i−2i00i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200002i−2i2−2−222−2−22000000000000
χ5344444-4-4-4-4400002222−22−22−22−2222220000000000000022−22−22220000000000000000000000000000000000
χ5444444-4-4-4-440000−22−2222222222−22−2200000000000000−222222−220000000000000000000000000000000000
χ554444-44-4-44-400002222−22−22−22−22222200000000000000−222222−220000000000000000000000000000000000
χ564444-44-4-44-40000−22−2222222222−22−220000000000000022−22−22220000000000000000000000000000000000
χ5744-4-44-4-444-444-4-400000000000000000000-4400000000000000000000000000000000000000
χ5844-4-4-44-44-4444-4-4000000000000000000004-400000000000000000000000000000000000000
χ594-44i−4i0000002i2−2i222−222ζ+2ζ3−2ζ−2ζ32ζ−2ζ3−2ζ+2ζ32ζ5−2ζ7−2ζ5+2ζ72ζ5+2ζ7−2ζ5−2ζ72-22i−2i2ζ2−2ζ22ζ6−2ζ600000000002ζ−2ζ2ζ5−2ζ52ζ7−2ζ72ζ3−2ζ300000000000000000000000000
χ604-44i−4i0000002i2−2i222−222ζ+2ζ3−2ζ−2ζ32ζ−2ζ3−2ζ+2ζ32ζ5−2ζ7−2ζ5+2ζ72ζ5+2ζ7−2ζ5−2ζ7-22−2i2i−2ζ22ζ2−2ζ62ζ60000000000−2ζ2ζ−2ζ52ζ5−2ζ72ζ7−2ζ32ζ300000000000000000000000000
χ614-44i−4i0000002i2−2i222−22−2ζ−2ζ32ζ+2ζ3−2ζ+2ζ32ζ−2ζ3−2ζ5+2ζ72ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ72-22i−2i2ζ2−2ζ22ζ6−2ζ60000000000−2ζ2ζ−2ζ52ζ5−2ζ72ζ7−2ζ32ζ300000000000000000000000000
χ624-44i−4i0000002i2−2i222−22−2ζ−2ζ32ζ+2ζ3−2ζ+2ζ32ζ−2ζ3−2ζ5+2ζ72ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ7-22−2i2i−2ζ22ζ2−2ζ62ζ600000000002ζ−2ζ2ζ5−2ζ52ζ7−2ζ72ζ3−2ζ300000000000000000000000000
χ634-44i−4i000000−2i22i2−22222ζ5−2ζ7−2ζ5+2ζ72ζ5+2ζ7−2ζ5−2ζ7−2ζ−2ζ32ζ+2ζ3−2ζ+2ζ32ζ−2ζ32-22i−2i−2ζ22ζ2−2ζ62ζ600000000002ζ5−2ζ5−2ζ2ζ2ζ3−2ζ3−2ζ72ζ700000000000000000000000000
χ644-44i−4i000000−2i22i2−22222ζ5−2ζ7−2ζ5+2ζ72ζ5+2ζ7−2ζ5−2ζ7−2ζ−2ζ32ζ+2ζ3−2ζ+2ζ32ζ−2ζ3-22−2i2i2ζ2−2ζ22ζ6−2ζ60000000000−2ζ52ζ52ζ−2ζ−2ζ32ζ32ζ7−2ζ700000000000000000000000000
χ654-44i−4i000000−2i22i2−2222−2ζ5+2ζ72ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ72ζ+2ζ3−2ζ−2ζ32ζ−2ζ3−2ζ+2ζ32-22i−2i−2ζ22ζ2−2ζ62ζ60000000000−2ζ52ζ52ζ−2ζ−2ζ32ζ32ζ7−2ζ700000000000000000000000000
χ664-44i−4i000000−2i22i2−2222−2ζ5+2ζ72ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ72ζ+2ζ3−2ζ−2ζ32ζ−2ζ3−2ζ+2ζ3-22−2i2i2ζ2−2ζ22ζ6−2ζ600000000002ζ5−2ζ5−2ζ2ζ2ζ3−2ζ3−2ζ72ζ700000000000000000000000000
χ674-4−4i4i0000002i2−2i2−22222ζ−2ζ3−2ζ+2ζ3−2ζ−2ζ32ζ+2ζ32ζ5+2ζ7−2ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ72-2−2i2i2ζ6−2ζ62ζ2−2ζ20000000000−2ζ32ζ32ζ7−2ζ7−2ζ52ζ52ζ−2ζ00000000000000000000000000
χ684-4−4i4i0000002i2−2i2−22222ζ−2ζ3−2ζ+2ζ3−2ζ−2ζ32ζ+2ζ32ζ5+2ζ7−2ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ7-222i−2i−2ζ62ζ6−2ζ22ζ200000000002ζ3−2ζ3−2ζ72ζ72ζ5−2ζ5−2ζ2ζ00000000000000000000000000
χ694-4−4i4i0000002i2−2i2−2222−2ζ+2ζ32ζ−2ζ32ζ+2ζ3−2ζ−2ζ3−2ζ5−2ζ72ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ72-2−2i2i2ζ6−2ζ62ζ2−2ζ200000000002ζ3−2ζ3−2ζ72ζ72ζ5−2ζ5−2ζ2ζ00000000000000000000000000
χ704-4−4i4i0000002i2−2i2−2222−2ζ+2ζ32ζ−2ζ32ζ+2ζ3−2ζ−2ζ3−2ζ5−2ζ72ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ7-222i−2i−2ζ62ζ6−2ζ22ζ20000000000−2ζ32ζ32ζ7−2ζ7−2ζ52ζ52ζ−2ζ00000000000000000000000000
χ714-4−4i4i000000−2i22i222−222ζ5+2ζ7−2ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ7−2ζ+2ζ32ζ−2ζ32ζ+2ζ3−2ζ−2ζ32-2−2i2i−2ζ62ζ6−2ζ22ζ200000000002ζ7−2ζ72ζ3−2ζ32ζ−2ζ2ζ5−2ζ500000000000000000000000000
χ724-4−4i4i000000−2i22i222−222ζ5+2ζ7−2ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ7−2ζ+2ζ32ζ−2ζ32ζ+2ζ3−2ζ−2ζ3-222i−2i2ζ6−2ζ62ζ2−2ζ20000000000−2ζ72ζ7−2ζ32ζ3−2ζ2ζ−2ζ52ζ500000000000000000000000000
χ734-4−4i4i000000−2i22i222−22−2ζ5−2ζ72ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ72ζ−2ζ3−2ζ+2ζ3−2ζ−2ζ32ζ+2ζ32-2−2i2i−2ζ62ζ6−2ζ22ζ20000000000−2ζ72ζ7−2ζ32ζ3−2ζ2ζ−2ζ52ζ500000000000000000000000000
χ744-4−4i4i000000−2i22i222−22−2ζ5−2ζ72ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ72ζ−2ζ3−2ζ+2ζ3−2ζ−2ζ32ζ+2ζ3-222i−2i2ζ6−2ζ62ζ2−2ζ200000000002ζ7−2ζ72ζ3−2ζ32ζ−2ζ2ζ5−2ζ500000000000000000000000000

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