Finite Group Databasebeta

← Group #145966

Character table — Group #145966

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444444444444444444441616161616161616161616161616161632323232
order124422244488888888444488881616161616161616161616161616161644881616161616161616161616162488
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ9222222222222-2-222-2-2-2-2-2-22-2-2222222222-2-2-2-2-2-2-2-200000000000000000000
χ10222222222222-2-222-2-2-2-2-2-22-2-22-2-2-2-2-2-2-2-22222222200000000000000000000
χ112222222222-2-222-2-222-2-2-2-2-222-2000000000000000022-2-20000000000000000
χ122222222222-2-222-2-222-2-2-2-2-222-20000000000000000-2-2220000000000000000
χ132222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000002i2i−2i−2i000000000000
χ142222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000−2i−2i2i2i000000000000
χ152222-2-222-2-2-2-200-2-200000020022i2i2i2i−2i−2i−2i−2i000000000000000022−2−2i2i2−i2−i20000
χ162222-2-222-2-2-2-200-2-200000020022i2i2i2i−2i−2i−2i−2i0000000000000000−2−222−i2−i2i2i20000
χ172222-2-222-2-2-2-200-2-20000002002−2i−2i−2i−2i2i2i2i2i000000000000000022−2−2−i2−i2i2i20000
χ182222-2-222-2-2-2-200-2-20000002002−2i−2i−2i−2i2i2i2i2i0000000000000000−2−222i2i2−i2−i20000
χ1922-2-22-2-22-222200-2-2000000-2002000000002222-2-2-2-200000000i2−i2i2−i2i2−i2i2−i20000
χ2022-2-22-2-22-222200-2-2000000-2002000000002222-2-2-2-200000000−i2i2−i2i2−i2i2−i2i20000
χ2122-2-22-2-22-222200-2-2000000-200200000000-2-2-2-2222200000000i2−i2i2−i2−i2i2−i2i20000
χ2222-2-22-2-22-222200-2-2000000-200200000000-2-2-2-2222200000000−i2i2−i2i2i2−i2i2−i20000
χ2322-2-2-22-222-22222-2-2-2-222-2-222-2-2000000000000000000000000000000002-200
χ2422-2-2-22-222-22222-2-2-2-222-2-222-2-200000000000000000000000000000000-2200
χ2522-2-2-22-222-222-2-2-2-222-2-2222-22-200000000000000000000000000000000002i−2i
χ2622-2-2-22-222-222-2-2-2-222-2-2222-22-20000000000000000000000000000000000−2i2i
χ2722-2-2-22-222-2-2-22222-2-2-2-222-22-220000000000000000000000002i−2i−2i2i00000000
χ2822-2-2-22-222-2-2-22222-2-2-2-222-22-22000000000000000000000000−2i2i2i−2i00000000
χ2922-2-2-22-222-2-2-2-2-2222222-2-2-2-22200000000000000000000000000002-2-220000
χ3022-2-2-22-222-2-2-2-2-2222222-2-2-2-2220000000000000000000000000000-222-20000
χ3122-2-2-2-22-222002200-2-200000-22022−2−222−2−222−2−222−2−2002i−2ii2−i2i2−i2000000000000
χ3222-2-2-2-22-222002200-2-200000-22022−2−222−2−222−2−222−2−200−2i2i−i2i2−i2i2000000000000
χ3322-2-2-2-22-222002200-2-200000-220−2−222−2−222−2−222−2−222002i−2i−i2i2−i2i2000000000000
χ3422-2-2-2-22-222002200-2-200000-220−2−222−2−222−2−222−2−22200−2i2ii2−i2i2−i2000000000000
χ3522-2-2-2-22-22200-2-20022000002-2022−2−222−2−2−2−222−2−2222-2002−2−22000000000000
χ3622-2-2-2-22-22200-2-20022000002-2022−2−222−2−2−2−222−2−222-2200−222−2000000000000
χ3722-2-2-2-22-22200-2-20022000002-20−2−222−2−22222−2−222−2−22-200−222−2000000000000
χ3822-2-2-2-22-22200-2-20022000002-20−2−222−2−22222−2−222−2−2-22002−2−22000000000000
χ3944444-4-4-44-40044004400000-4-40000000000000000000000000000000000000
χ4044444-4-4-44-400-4-400-4-400000440000000000000000000000000000000000000
χ414444-44-4-4-440000000000000000000000002222−22−22−22−22222200000000000000000000
χ424444-44-4-4-44000000000000000000000000−22−2222222222−22−2200000000000000000000
χ434444-4-444-4-4440044000000-400-4000000000000000000000000000000000000
χ4444-4-4444-4-4-400000000000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000
χ4544-4-4444-4-4-40000000000000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000
χ4644-4-44-4-44-44-4-40044000000400-4000000000000000000000000000000000000
χ474-44i−4i00000022−2222−222i2−2i22i2−2i22-22i−2i00002ζ−2ζ2ζ5−2ζ52ζ7−2ζ72ζ3−2ζ3ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ700000000000000000000
χ484-44i−4i00000022−2222−222i2−2i22i2−2i22-22i−2i0000−2ζ2ζ−2ζ52ζ5−2ζ72ζ7−2ζ32ζ3−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ700000000000000000000
χ494-44i−4i00000022−22−22222i2−2i2−2i22i2-22−2i2i00002ζ−2ζ2ζ5−2ζ52ζ7−2ζ72ζ3−2ζ3−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ700000000000000000000
χ504-44i−4i00000022−22−22222i2−2i2−2i22i2-22−2i2i0000−2ζ2ζ−2ζ52ζ5−2ζ72ζ7−2ζ32ζ3ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ700000000000000000000
χ514-44i−4i000000−222222−22−2i22i22i2−2i2-22−2i2i00002ζ5−2ζ5−2ζ2ζ2ζ3−2ζ3−2ζ72ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ700000000000000000000
χ524-44i−4i000000−222222−22−2i22i22i2−2i2-22−2i2i0000−2ζ52ζ52ζ−2ζ−2ζ32ζ32ζ7−2ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ700000000000000000000
χ534-44i−4i000000−2222−2222−2i22i2−2i22i22-22i−2i00002ζ5−2ζ5−2ζ2ζ2ζ3−2ζ3−2ζ72ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ700000000000000000000
χ544-44i−4i000000−2222−2222−2i22i2−2i22i22-22i−2i0000−2ζ52ζ52ζ−2ζ−2ζ32ζ32ζ7−2ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ700000000000000000000
χ554-4−4i4i00000022−2222−22−2i22i2−2i22i22-2−2i2i00002ζ7−2ζ72ζ3−2ζ32ζ−2ζ2ζ5−2ζ5−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ700000000000000000000
χ564-4−4i4i00000022−2222−22−2i22i2−2i22i22-2−2i2i0000−2ζ72ζ7−2ζ32ζ3−2ζ2ζ−2ζ52ζ5ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ700000000000000000000
χ574-4−4i4i00000022−22−2222−2i22i22i2−2i2-222i−2i00002ζ7−2ζ72ζ3−2ζ32ζ−2ζ2ζ5−2ζ5ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ700000000000000000000
χ584-4−4i4i00000022−22−2222−2i22i22i2−2i2-222i−2i0000−2ζ72ζ7−2ζ32ζ3−2ζ2ζ−2ζ52ζ5−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ700000000000000000000
χ594-4−4i4i000000−222222−222i2−2i2−2i22i2-222i−2i00002ζ3−2ζ3−2ζ72ζ72ζ5−2ζ5−2ζ2ζζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ700000000000000000000
χ604-4−4i4i000000−222222−222i2−2i2−2i22i2-222i−2i0000−2ζ32ζ32ζ7−2ζ7−2ζ52ζ52ζ−2ζ−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ700000000000000000000
χ614-4−4i4i000000−2222−22222i2−2i22i2−2i22-2−2i2i00002ζ3−2ζ3−2ζ72ζ72ζ5−2ζ5−2ζ2ζ−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ700000000000000000000
χ624-4−4i4i000000−2222−22222i2−2i22i2−2i22-2−2i2i0000−2ζ32ζ32ζ7−2ζ7−2ζ52ζ52ζ−2ζζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ700000000000000000000

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