Finite Group Databasebeta

← Group #72324259

Character table — Group #72324259

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11222444488888888816161616161616161616161616161616161616161616161616161616161632326464646464646464646464646464128128128128
order12222222222222222222222222244444444444444444444444444444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ411111111111111111111111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-111-1-11-1-111-1-111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1
χ6111111111111111111111-1-111-1-11-1-111-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-111
χ7111111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1111111-1-1
χ911111111111111-1-1-1-11-1-1111111111111111111111111111-1-1-1-1-1-1-1-1ii−i−iii−i−ii−ii−i
χ1011111111111111-1-1-1-11-1-1111111111111111111111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−ii−ii
χ1111111111111111-1-1-1-11-1-111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−iii−i−i−ii−ii
χ1211111111111111-1-1-1-11-1-111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii−i−iiii−ii−i
χ1311111111111111-1-1-1-11-1-1-1-111-1-11-1-111-1-111-1-1-1-11111-1-1-1-1-1-111-1-111ii−i−i−i−iiii−i−ii
χ1411111111111111-1-1-1-11-1-1-1-111-1-11-1-111-1-111-1-1-1-11111-1-1-1-1-1-111-1-111−i−iiiii−i−i−iii−i
χ1511111111111111-1-1-1-11-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1ii−i−i−i−iii−iii−i
χ1611111111111111-1-1-1-11-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1−i−iiiii−i−ii−i−ii
χ17222222222222222222-2222-20000-22-20000-2-222-2-200000000-2-22-20000000000000000
χ18222222222222222222-222-220000-2-220000-2-2-2-22200000000-2-2-220000000000000000
χ1922222222222222-2-2-2-2-2-2-22-20000-22-20000-2-222-2-20000000022-220000000000000000
χ2022222222222222-2-2-2-2-2-2-2-220000-2-220000-2-2-2-22200000000222-20000000000000000
χ21222222222-2-2-2-2222-2-222-2002200200-2-200-2-2000022-2-200002-2002-200000000000000
χ22222222222-2-2-2-2222-2-222-200-2-2002002200-2-20000-2-22200002-200-2200000000000000
χ23222222222-2-2-2-2222-2-2-22-200002-2-200002-2220000000022-2-2-2200002-2000000000000
χ24222222222-2-2-2-2222-2-2-22-20000-22-20000-222200000000-2-222-220000-22000000000000
χ25222222222-2-2-2-22-2-2222-22002200200-2-200-2-2000022-2-20000-2200-2200000000000000
χ26222222222-2-2-2-22-2-2222-2200-2-2002002200-2-20000-2-2220000-22002-200000000000000
χ27222222222-2-2-2-22-2-222-2-2200002-2-200002-2220000000022-2-22-20000-22000000000000
χ28222222222-2-2-2-22-2-222-2-220000-22-20000-222200000000-2-2222-200002-2000000000000
χ294444444-4-40000-40000400004400-4000000000000-4-400000000000000000000000000
χ304444444-4-40000-4000040000-4-400-40000000000004400000000000000000000000000
χ314444444-4-40000-40000-400000000400440000000000-4-4000000000000000000000000
χ324444444-4-40000-40000-400000000400-4-4000000000044000000000000000000000000
χ3344444-4-44444-4-4-4000000004000000400000000-4-40000000000000000000000000000
χ3444444-4-44444-4-4-400000000-4000000-400000000440000000000000000000000000000
χ3544444-4-444-4-444-40000000400000040000000-4-4000000000000000000000000000000
χ3644444-4-444-4-444-40000000-4000000-4000000044000000000000000000000000000000
χ3744444-4-4-4-400004000000000000400000044-40000000000-4-400000000000000000000
χ3844444-4-4-4-400004000000000000-4000000-44-400000000004400000000000000000000
χ3944444-4-4-4-40000400000000000400000040-4400000000-4-40000000000000000000000
χ4044444-4-4-4-40000400000000000-4000000-40-4400000000440000000000000000000000
χ4144-4-44004-4004-400000000002-2220002-2-2-2004-4002-22-22-22-200000000000000000000
χ4244-4-44004-4004-400000000002-2-2-20002-22200-44002-22-2-22-2200000000000000000000
χ4344-4-44004-4004-40000000000-2222000-22-2-200-4400-22-222-22-200000000000000000000
χ4444-4-44004-4004-40000000000-22-2-2000-2222004-400-22-22-22-2200000000000000000000
χ4544-4-44004-400-4400000000402-22-20-40-22-220000002-2-222-2-2200000000000000000000
χ4644-4-44004-400-440000000040-22-220-402-22-2000000-222-2-222-200000000000000000000
χ4744-4-44004-400-4400000000-402-2-22040-222-20000002-2-22-222-200000000000000000000
χ4844-4-44004-400-4400000000-40-222-20402-2-22000000-222-22-2-2200000000000000000000
χ4944-4-4400-444-40000000000002-222000-22-2-200004-4-222-2-22-2200000000000000000000
χ5044-4-4400-444-40000000000002-2-2-2000-22220000-44-222-22-22-200000000000000000000
χ5144-4-4400-444-4000000000000-22220002-2-2-20000-442-2-22-22-2200000000000000000000
χ5244-4-4400-444-4000000000000-22-2-20002-22200004-42-2-222-22-200000000000000000000
χ5344-4-4400-44-440000000000042-2-2200-42-22-2000000-22-222-2-2200000000000000000000
χ5444-4-4400-44-44000000000004-222-200-4-22-220000002-22-2-222-200000000000000000000
χ5544-4-4400-44-4400000000000-42-22-20042-2-22000000-22-22-222-200000000000000000000
χ5644-4-4400-44-4400000000000-4-22-22004-222-20000002-22-22-2-2200000000000000000000
χ57888-8-8000000000004400-40000000000000000000000000000000000000002-22-20000
χ58888-8-8000000000004400-4000000000000000000000000000000000000000-22-220000
χ59888-8-800000000000-4-40040000000000000000000000000000000000000002i−2i−2i2i0000
χ60888-8-800000000000-4-4004000000000000000000000000000000000000000−2i2i2i−2i0000
χ6188-88-800000000044000-40000000000000000000000000000000000002-22-200000000
χ6288-88-800000000044000-4000000000000000000000000000000000000-22-2200000000
χ6388-88-8000000000-4-400040000000000000000000000000000000000002i−2i−2i2i00000000
χ6488-88-8000000000-4-40004000000000000000000000000000000000000−2i2i2i−2i00000000
χ6516-160008-80000000008-800000000000000000000000000000000000000000000000000
χ6616-160008-8000000000-8800000000000000000000000000000000000000000000000000
χ6716-16000-8800000008-80000000000000000000000000000000000000000000000000000
χ6816-16000-880000000-880000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).