Finite Group Databasebeta

← Group #140262

Character table — Group #140262

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order12442224448888888816161616161616164444888816161616161616161616161644448888161616161616161616161616161616164488
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ911-1-1-1-1111-1-1-11111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iiiii−i−i−i−iii−i−iii−i−i1111-1-1-1-1ii−i−i11-1-11-1i−i
χ1011-1-1-1-1111-1-1-11111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iiiii−i−i−i−iii−i−iii−i−i1111-1-1-1-1−i−iii-1-111-11−ii
χ1111-1-1-1-1111-1-1-11111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iiiii−i−i−i−i−i−iii−i−iii-1-1-1-11111ii−i−i11-1-1-11−ii
χ1211-1-1-1-1111-1-1-11111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iiiii−i−i−i−i−i−iii−i−iii-1-1-1-11111−i−iii-1-1111-1i−i
χ1311-1-1-1-1111-1-1-11111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−i−i−iiiiiii−i−iii−i−i-1-1-1-11111ii−i−i-1-1111-1−ii
χ1411-1-1-1-1111-1-1-11111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−i−i−iiiiiii−i−iii−i−i-1-1-1-11111−i−iii11-1-1-11i−i
χ1511-1-1-1-1111-1-1-11111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−i−i−iiiii−i−iii−i−iii1111-1-1-1-1ii−i−i-1-111-11i−i
χ1611-1-1-1-1111-1-1-11111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−i−i−iiiii−i−iii−i−iii1111-1-1-1-1−i−iii11-1-11-1−ii
χ1722222222222222-2-2-2-222222222-2-2-2-22-2-222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22-2-22-2-2-2-2222222220000000000000000000000000000
χ192222222222-2-2-2-2222200000000-2-2-2-2-222-20000000000002222-2-2-2-200000000000000000000
χ202222222222-2-2-2-2222200000000-2-2-2-2-222-2000000000000-2-2-2-2222200000000000000000000
χ212222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2322222-2-22-2-20000222222−2−222−2−200000-2-202−22−222−2−222−2−22i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i2000000000000
χ2422222-2-22-2-20000222222−2−222−2−200000-2-202−22−222−2−222−2−2−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i2000000000000
χ2522222-2-22-2-200002222−2−222−2−22200000-2-20−22−22−2−222−2−2222i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i2000000000000
χ2622222-2-22-2-200002222−2−222−2−22200000-2-20−22−22−2−222−2−222−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i2000000000000
χ2722222-2-22-2-20000-2-2-2-222−2−222−2−2000002202−22−2−2−222−2−22200002-22-22−2−222−2−22000000000000
χ2822222-2-22-2-20000-2-2-2-222−2−222−2−2000002202−22−2−2−222−2−2220000-22-22−222−2−222−2000000000000
χ2922222-2-22-2-20000-2-2-2-2−2−222−2−22200000220−22−2222−2−222−2−200002-22-2−222−2−222−2000000000000
χ3022222-2-22-2-20000-2-2-2-2−2−222−2−22200000220−22−2222−2−222−2−20000-22-222−2−222−2−22000000000000
χ312222-22-2-22-222220000222222220000-200-2-2-2-2-2000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ322222-22-2-22-222220000222222220000-200-2-2-2-2-2000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ332222-22-2-22-222220000-2-2-2-2-2-2-2-20000-200-22222000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ342222-22-2-22-222220000-2-2-2-2-2-2-2-20000-200-22222000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ3522-2-22-2-2-222-2-22200002i2i2i2i−2i−2i−2i−2i0000-2002−2i−2i2i2i0000000000000000000000002−2−22−i2i2i2−i20000
χ3622-2-22-2-2-222-2-22200002i2i2i2i−2i−2i−2i−2i0000-2002−2i−2i2i2i000000000000000000000000−222−2i2−i2−i2i20000
χ3722-2-22-2-2-222-2-2220000−2i−2i−2i−2i2i2i2i2i0000-20022i2i−2i−2i0000000000000000000000002−2−22i2−i2−i2i20000
χ3822-2-22-2-2-222-2-2220000−2i−2i−2i−2i2i2i2i2i0000-20022i2i−2i−2i000000000000000000000000−222−2−i2i2i2−i20000
χ3922-2-2-22-22-22000022-2-2i2i2−i2−i2−i2−i2i2i200000-220i2−i2−i2i2i2i2−i2−i2−i2−i2i2i22-2-220000−i2i2−i2i2i2−i2i2−i2000000000000
χ4022-2-2-22-22-22000022-2-2i2i2−i2−i2−i2−i2i2i200000-220i2−i2−i2i2i2i2−i2−i2−i2−i2i2i2-222-20000i2−i2i2−i2−i2i2−i2i2000000000000
χ4122-2-2-22-22-22000022-2-2−i2−i2i2i2i2i2−i2−i200000-220−i2i2i2−i2−i2−i2i2i2i2i2−i2−i22-2-220000i2−i2i2−i2−i2i2−i2i2000000000000
χ4222-2-2-22-22-22000022-2-2−i2−i2i2i2i2i2−i2−i200000-220−i2i2i2−i2−i2−i2i2i2i2i2−i2−i2-222-20000−i2i2−i2i2i2−i2i2−i2000000000000
χ4322-2-2-22-22-220000-2-222i2i2−i2−i2−i2−i2i2i2000002-20i2−i2−i2i2−i2−i2i2i2i2i2−i2−i200002i−2i−2i2i2−2−22−222−2000000000000
χ4422-2-2-22-22-220000-2-222i2i2−i2−i2−i2−i2i2i2000002-20i2−i2−i2i2−i2−i2i2i2i2i2−i2−i20000−2i2i2i−2i−222−22−2−22000000000000
χ4522-2-2-22-22-220000-2-222−i2−i2i2i2i2i2−i2−i2000002-20−i2i2i2−i2i2i2−i2−i2−i2−i2i2i200002i−2i−2i2i−222−22−2−22000000000000
χ4622-2-2-22-22-220000-2-222−i2−i2i2i2i2i2−i2−i2000002-20−i2i2i2−i2i2i2−i2−i2−i2−i2i2i20000−2i2i2i−2i2−2−22−222−2000000000000
χ4722-2-2-2-2222-222-2-222-2-200000000-2-222-22-220000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ4822-2-2-2-2222-222-2-222-2-200000000-2-222-22-22000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ4922-2-2-2-2222-222-2-2-2-2220000000022-2-2-2-222000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ5022-2-2-2-2222-222-2-2-2-2220000000022-2-2-2-22200000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ5122-2-2-2-2222-2-2-222-2-2222i2i2i2i−2i−2i−2i−2i-2-2222-22-22i2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000
χ5222-2-2-2-2222-2-2-222-2-222−2i−2i−2i−2i2i2i2i2i-2-2222-22-2−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000
χ534444-44-4-44-4-4-4-4-4000000000000000040040000000000000000000000000000000000000000
χ544444-4-44-4-44000000002222−22−222222−22−2200000000−2222−2222000000000000000000000000000000000000
χ554444-4-44-4-4400000000−22−222222−22−2222220000000022−2222−22000000000000000000000000000000000000
χ5644-4-4444-4-4-4000000002i22i2−2i2−2i2−2i2−2i22i22i200000000−2i22i22i2−2i2000000000000000000000000000000000000
χ5744-4-4444-4-4-400000000−2i2−2i22i22i22i22i2−2i2−2i2000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ5844-4-44-4-4-44444-4-40000000000000000400-40000000000000000000000000000000000000000
χ594-44i−4i0000002i2−2i222−222i2−2i222−222ζ+2ζ3−2ζ−2ζ32ζ5−2ζ7−2ζ5+2ζ72ζ5+2ζ7−2ζ5−2ζ72ζ−2ζ3−2ζ+2ζ32i−2i2-200000000ζ−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−ζ70000000000000000000000000000
χ604-44i−4i0000002i2−2i222−222i2−2i222−22−2ζ−2ζ32ζ+2ζ3−2ζ5+2ζ72ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ+2ζ32ζ−2ζ32i−2i2-200000000−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+ζ70000000000000000000000000000
χ614-44i−4i0000002i2−2i222−22−2i22i2−22222ζ+2ζ3−2ζ−2ζ32ζ5−2ζ7−2ζ5+2ζ72ζ5+2ζ7−2ζ5−2ζ72ζ−2ζ3−2ζ+2ζ3−2i2i-2200000000−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+ζ70000000000000000000000000000
χ624-44i−4i0000002i2−2i222−22−2i22i2−2222−2ζ−2ζ32ζ+2ζ3−2ζ5+2ζ72ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ+2ζ32ζ−2ζ3−2i2i-2200000000ζ−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−ζ70000000000000000000000000000
χ634-44i−4i000000−2i22i2−22222i2−2i222−222ζ5−2ζ7−2ζ5+2ζ7−2ζ−2ζ32ζ+2ζ3−2ζ+2ζ32ζ−2ζ32ζ5+2ζ7−2ζ5−2ζ7−2i2i-2200000000−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−ζ70000000000000000000000000000
χ644-44i−4i000000−2i22i2−22222i2−2i222−22−2ζ5+2ζ72ζ5−2ζ72ζ+2ζ3−2ζ−2ζ32ζ−2ζ3−2ζ+2ζ3−2ζ5−2ζ72ζ5+2ζ7−2i2i-2200000000ζ−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+ζ70000000000000000000000000000
χ654-44i−4i000000−2i22i2−2222−2i22i2−22222ζ5−2ζ7−2ζ5+2ζ7−2ζ−2ζ32ζ+2ζ3−2ζ+2ζ32ζ−2ζ32ζ5+2ζ7−2ζ5−2ζ72i−2i2-200000000ζ−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+ζ70000000000000000000000000000
χ664-44i−4i000000−2i22i2−2222−2i22i2−2222−2ζ5+2ζ72ζ5−2ζ72ζ+2ζ3−2ζ−2ζ32ζ−2ζ3−2ζ+2ζ3−2ζ5−2ζ72ζ5+2ζ72i−2i2-200000000−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−ζ70000000000000000000000000000
χ674-4−4i4i0000002i2−2i2−22222i2−2i2−22222ζ−2ζ3−2ζ+2ζ32ζ5+2ζ7−2ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ7−2ζ−2ζ32ζ+2ζ3−2i2i2-200000000−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+ζ70000000000000000000000000000
χ684-4−4i4i0000002i2−2i2−22222i2−2i2−2222−2ζ+2ζ32ζ−2ζ3−2ζ5−2ζ72ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ72ζ+2ζ3−2ζ−2ζ3−2i2i2-200000000ζ+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−ζ70000000000000000000000000000
χ694-4−4i4i0000002i2−2i2−2222−2i22i222−222ζ−2ζ3−2ζ+2ζ32ζ5+2ζ7−2ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ7−2ζ−2ζ32ζ+2ζ32i−2i-2200000000ζ+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−ζ70000000000000000000000000000
χ704-4−4i4i0000002i2−2i2−2222−2i22i222−22−2ζ+2ζ32ζ−2ζ3−2ζ5−2ζ72ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ72ζ+2ζ3−2ζ−2ζ32i−2i-2200000000−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+ζ70000000000000000000000000000
χ714-4−4i4i000000−2i22i222−222i2−2i2−22222ζ5+2ζ7−2ζ5−2ζ7−2ζ+2ζ32ζ−2ζ32ζ+2ζ3−2ζ−2ζ3−2ζ5+2ζ72ζ5−2ζ72i−2i-2200000000ζ+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+ζ70000000000000000000000000000
χ724-4−4i4i000000−2i22i222−222i2−2i2−2222−2ζ5−2ζ72ζ5+2ζ72ζ−2ζ3−2ζ+2ζ3−2ζ−2ζ32ζ+2ζ32ζ5−2ζ7−2ζ5+2ζ72i−2i-2200000000−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−ζ70000000000000000000000000000
χ734-4−4i4i000000−2i22i222−22−2i22i222−222ζ5+2ζ7−2ζ5−2ζ7−2ζ+2ζ32ζ−2ζ32ζ+2ζ3−2ζ−2ζ3−2ζ5+2ζ72ζ5−2ζ7−2i2i2-200000000−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−ζ70000000000000000000000000000
χ744-4−4i4i000000−2i22i222−22−2i22i222−22−2ζ5−2ζ72ζ5+2ζ72ζ−2ζ3−2ζ+2ζ3−2ζ−2ζ32ζ+2ζ32ζ5−2ζ7−2ζ5+2ζ7−2i2i2-200000000ζ+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+ζ70000000000000000000000000000

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