Finite Group Databasebeta

← Group #72324256

Character table — Group #72324256

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11222444488888888816161616161616161616161616161616323232323264646464646464646464646464646464128128128128
order12222222222222222222222444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-11-111111111-11-1-1-1-11-1-1-111-1-1ii−i−iii−i−iii−i−i
χ6111111111111111111111-1-11-111111111-11-1-1-1-11-1-1-111-1-1−i−iii−i−iii−i−iii
χ7111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-11-1-1-1-11-111-1-111ii−i−iii−i−i−i−iii
χ8111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-11-1-1-1-11-111-1-111−i−iii−i−iiiii−i−i
χ911111111111111111111-11-1-1111111111-1-11-1-1-1-11-1-1-1-111i−ii−ii−ii−ii−ii−i
χ1011111111111111111111-11-1-1111111111-1-11-1-1-1-11-1-1-1-111−ii−ii−ii−ii−ii−ii
χ1111111111111111111111-11-1-11-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1i−ii−ii−ii−i−ii−ii
χ1211111111111111111111-11-1-11-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1−ii−ii−ii−iii−ii−i
χ1311111111111111111111-1-11-1-1111111111-1-1111-1-111-1-1-1-11-1-111-1-111-1-11
χ1411111111111111111111-1-11-1-1111111111-1-1111-1-111-1-1-1-1-111-1-111-1-111-1
χ1511111111111111111111-1-11-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111111-1-111-1-11-111-1
χ1611111111111111111111-1-11-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-11111-111-1-111-11-1-11
χ1722222222222222-2-2-2-2-2-20020000000000200-2-220000000002200-2-200000
χ1822222222222222-2-2-2-2-2-20020000000000200-2-22000000000-2-2002200000
χ1922222222222222-2-2-2-2-2-200-20000000000-20022-20000000002i−2i00−2i2i00000
χ2022222222222222-2-2-2-2-2-200-20000000000-20022-2000000000−2i2i002i−2i00000
χ212222222222-2-2-2-22222-2-222222000000002222-2-2-2-2000000000000000000
χ222222222222-2-2-2-22222-2-22-2-22-200000000-22-2-222-22000000000000000000
χ232222222222-2-2-2-22222-2-2-22-2-2200000000-2-22-2222-2000000000000000000
χ242222222222-2-2-2-22222-2-2-2-22-2-2000000002-2-22-2-222000000000000000000
χ252222222222-2-2-2-2-2-2-2-2220020000000000200-22-2000000002002-200-20000
χ262222222222-2-2-2-2-2-2-2-2220020000000000200-22-200000000-200-220020000
χ272222222222-2-2-2-2-2-2-2-22200-20000000000-2002-22000000002i00−2i−2i002i0000
χ282222222222-2-2-2-2-2-2-2-22200-20000000000-2002-2200000000−2i002i2i00−2i0000
χ294444444-4-4-40000000000004002222-2-2-2-2-400000002-20000000000000000
χ304444444-4-4-4000000000000400-2-2-2-22222-40000000-220000000000000000
χ314444444-4-4-4000000000000-4002222-2-2-2-240000000-220000000000000000
χ324444444-4-4-4000000000000-400-2-2-2-22222400000002-20000000000000000
χ3344444-4-444-400004-44-400040040000000000-400000000000000000000000
χ3444444-4-444-400004-44-4000-400-40000000000400000000000000000000000
χ3544444-4-444-40000-44-440040040000000000-4000000000000000000000000
χ3644444-4-444-40000-44-4400-400-400000000004000000000000000000000000
χ3744-44-4004-400000040-400400-402i2i−2i−2i2i2i−2i−2i00000000002i−2i00000000000000
χ3844-44-4004-400000040-400400-40−2i−2i2i2i−2i−2i2i2i0000000000−2i2i00000000000000
χ3944-44-4004-400000040-400-400402i2i−2i−2i2i2i−2i−2i0000000000−2i2i00000000000000
χ4044-44-4004-400000040-400-40040−2i−2i2i2i−2i−2i2i2i00000000002i−2i00000000000000
χ4144-44-400-440000040-40000400-42i2i−2i−2i−2i−2i2i2i0000000000002i−2i000000000000
χ4244-44-400-440000040-40000400-4−2i−2i2i2i2i2i−2i−2i000000000000−2i2i000000000000
χ4344-44-400-440000040-40000-40042i2i−2i−2i−2i−2i2i2i000000000000−2i2i000000000000
χ4444-44-400-440000040-40000-4004−2i−2i2i2i2i2i−2i−2i0000000000002i−2i000000000000
χ4588888-8-8-8-880000000000000000000000000000000000000000000000000
χ46888-8-800000000000004-40000000004i−4i4i−4i00000000000000000000000000
χ47888-8-800000000000004-4000000000−4i4i−4i4i00000000000000000000000000
χ48888-8-80000000000000-44000004i−4i4i−4i000000000000000000000000000000
χ49888-8-80000000000000-4400000−4i4i−4i4i000000000000000000000000000000
χ5088-88-8008-8000000-80800000000000000000000000000000000000000000
χ5188-88-800-8800000-808000000000000000000000000000000000000000000
χ5288-8-880000044-4-40000000000000004-4-4400000000000000000000000000
χ5388-8-880000044-4-4000000000000000-444-400000000000000000000000000
χ5488-8-8800000-4-444000000000004-4-44000000000000000000000000000000
χ5588-8-8800000-4-44400000000000-444-4000000000000000000000000000000
χ5616-160008-8000008-8000000000000000000000000000000000000000000000
χ5716-160008-800000-88000000000000000000000000000000000000000000000
χ5816-16000-880008-800000000000000000000000000000000000000000000000
χ5916-16000-88000-8800000000000000000000000000000000000000000000000

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