Finite Group Databasebeta

← Group #72251447

Character table — Group #72251447

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11222444444881616161616161616161616161616161616161616161616323232323232326464646464641122244444488161616161616161616161616161616161616161616161632323232323232646464646464
order12222224444442222222444488888888888844444444488882222222444444222222244448888888888884444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1
χ311111111111111111-1-111111111111111111-1-1-11111-1-1-1-1-1-111111111111111111-1-111111111111111111-1-1-11111-1-1-1-1-1-1
χ411111111111111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111111111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ5111111111111111-1-1111-1-111-1-1-1-11111-1-1-1-111111-1-111-1-1-1-1111111111111111-1-1111-1-111-1-1-1-11111-1-1-1-111111-1-111-1-1-1-1
χ6111111111111111-1-1111-1-111-1-1-1-1-1-1-1-11111111-1-111-1-1-1-111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-11111111-1-111-1-1-1-111
χ7111111111111111-1-1-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111111111111111111-1-1-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111
χ8111111111111111-1-1-1-11-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1111111111111111-1-1-1-11-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1
χ911111-1-11-11-111111-111-11-1-1-111-1-1ii−i−iii−i−i-1-11i−ii−ii−i1-1i−i11111-1-11-11-111111-111-11-1-1-111-1-1ii−i−iii−i−i-1-11i−ii−ii−i1-1i−i
χ1011111-1-11-11-111111-111-11-1-1-111-1-1−i−iii−i−iii-1-11−ii−ii−ii1-1−ii11111-1-11-11-111111-111-11-1-1-111-1-1−i−iii−i−iii-1-11−ii−ii−ii1-1−ii
χ1111111-1-11-11-111111-1-1-1-11-1-1-111-1-1ii−i−iii−i−i11-1i−ii−i−ii-11−ii11111-1-11-11-111111-1-1-1-11-1-1-111-1-1ii−i−iii−i−i11-1i−ii−i−ii-11−ii
χ1211111-1-11-11-111111-1-1-1-11-1-1-111-1-1−i−iii−i−iii11-1−ii−iii−i-11i−i11111-1-11-11-111111-1-1-1-11-1-1-111-1-1−i−iii−i−iii11-1−ii−iii−i-11i−i
χ1311111-1-11-11-11111-1111-1-11-1-1-1-111ii−i−i−i−iii-1-11i−i−iii−i-11−ii11111-1-11-11-11111-1111-1-11-1-1-1-111ii−i−i−i−iii-1-11i−i−iii−i-11−ii
χ1411111-1-11-11-11111-1111-1-11-1-1-1-111−i−iiiii−i−i-1-11−iii−i−ii-11i−i11111-1-11-11-11111-1111-1-11-1-1-1-111−i−iiiii−i−i-1-11−iii−i−ii-11i−i
χ1511111-1-11-11-11111-11-1-1-1-11-1-1-1-111ii−i−i−i−iii11-1i−i−ii−ii1-1i−i11111-1-11-11-11111-11-1-1-1-11-1-1-1-111ii−i−i−i−iii11-1i−i−ii−ii1-1i−i
χ1611111-1-11-11-11111-11-1-1-1-11-1-1-1-111−i−iiiii−i−i11-1−iii−ii−i1-1−ii11111-1-11-11-11111-11-1-1-1-11-1-1-1-111−i−iiiii−i−i11-1−iii−ii−i1-1−ii
χ172222222222222-2-22200-2222-2-2-2-2-20000000000000000000002222222222222-2-22200-2222-2-2-2-2-2000000000000000000000
χ182222222222222-2-2-2-200-2-2-22-222220000000000000000000002222222222222-2-2-2-200-2-2-22-22222000000000000000000000
χ1922222222222-2-22-20000200-2-2000022220000000-2-20000000022222222222-2-22-20000200-2-2000022220000000-2-200000000
χ2022222222222-2-22-20000200-2-20000-2-2-2-20000000220000000022222222222-2-22-20000200-2-20000-2-2-2-200000002200000000
χ2122222222222-2-2-220000-200-2200000000222200000-2-200000022222222222-2-2-220000-200-2200000000222200000-2-2000000
χ2222222222222-2-2-220000-200-2200000000-2-2-2-2000002200000022222222222-2-2-220000-200-2200000000-2-2-2-20000022000000
χ2322222-2-22-22-222-2-22-20022-2-22-2-22200000000000000000000022222-2-22-22-222-2-22-20022-2-22-2-222000000000000000000000
χ2422222-2-22-22-222-2-2-22002-22-2222-2-200000000000000000000022222-2-22-22-222-2-2-22002-22-2222-2-2000000000000000000000
χ2522222-2-22-22-2-2-22-20000-2002200002i2i−2i−2i0000000−2i2i0000000022222-2-22-22-2-2-22-20000-2002200002i2i−2i−2i0000000−2i2i00000000
χ2622222-2-22-22-2-2-22-20000-200220000−2i−2i2i2i00000002i−2i0000000022222-2-22-22-2-2-22-20000-200220000−2i−2i2i2i00000002i−2i00000000
χ2722222-2-22-22-2-2-2-2200002002-2000000002i2i−2i−2i00000−2i2i00000022222-2-22-22-2-2-2-2200002002-2000000002i2i−2i−2i00000−2i2i000000
χ2822222-2-22-22-2-2-2-2200002002-200000000−2i−2i2i2i000002i−2i00000022222-2-22-22-2-2-2-2200002002-200000000−2i−2i2i2i000002i−2i000000
χ294444444-4-4-4-400000022000000000000000002-2-200000000004444444-4-4-4-400000022000000000000000002-2-20000000000
χ304444444-4-4-4-4000000-2-200000000000000000-22200000000004444444-4-4-4-4000000-2-200000000000000000-2220000000000
χ3144444-4-4-44-440000002200000000000000000-22-2000000000044444-4-4-44-440000002200000000000000000-22-20000000000
χ3244444-4-4-44-44000000-2-2000000000000000002-22000000000044444-4-4-44-44000000-2-2000000000000000002-220000000000
χ33444-4-400040-400000000000002-22-22i−2i2i−2i2i−2i2i−2i0000000000000444-4-400040-400000000000002-22-22i−2i2i−2i2i−2i2i−2i0000000000000
χ34444-4-400040-400000000000002-22-2−2i2i−2i2i−2i2i−2i2i0000000000000444-4-400040-400000000000002-22-2−2i2i−2i2i−2i2i−2i2i0000000000000
χ35444-4-400040-40000000000000-22-222i−2i2i−2i−2i2i−2i2i0000000000000444-4-400040-40000000000000-22-222i−2i2i−2i−2i2i−2i2i0000000000000
χ36444-4-400040-40000000000000-22-22−2i2i−2i2i2i−2i2i−2i0000000000000444-4-400040-40000000000000-22-22−2i2i−2i2i2i−2i2i−2i0000000000000
χ37444-4-4000-40400000000000002-2-222-2-222-2-220000000000000444-4-4000-40400000000000002-2-222-2-222-2-220000000000000
χ38444-4-4000-40400000000000002-2-22-222-2-222-20000000000000444-4-4000-40400000000000002-2-22-222-2-222-20000000000000
χ39444-4-4000-4040000000000000-222-22-2-22-222-20000000000000444-4-4000-4040000000000000-222-22-2-22-222-20000000000000
χ40444-4-4000-4040000000000000-222-2-222-22-2-220000000000000444-4-4000-4040000000000000-222-2-222-22-2-220000000000000
χ4144-4-4400-40404-400040000-400000000000000000000000000044-4-4400-40404-400040000-4000000000000000000000000000
χ4244-4-4400-40404-4000-40000400000000000000000000000000044-4-4400-40404-4000-400004000000000000000000000000000
χ4344-4-4400-4040-440040000-4000000000000000000000000000044-4-4400-4040-440040000-40000000000000000000000000000
χ4444-4-4400-4040-4400-400004000000000000000000000000000044-4-4400-4040-4400-4000040000000000000000000000000000
χ4588-88-88-800000000000000000000000000000000000000000088-88-88-8000000000000000000000000000000000000000000
χ4688-88-8-8800000000000000000000000000000000000000000088-88-8-88000000000000000000000000000000000000000000
χ4788-8-880080-800000000000000000000000000000000000000088-8-880080-8000000000000000000000000000000000000000
χ4816-160000000000000004-400000000000000000000000000000016-160000000000000004-4000000000000000000000000000000
χ4916-16000000000000000-4400000000000000000000000000000016-16000000000000000-44000000000000000000000000000000
χ501111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ511111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1111111-1-111
χ5211111111111111111-1-111111111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111111
χ5311111111111111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111111111111111-1-111-1-1
χ54111111111111111-1-1111-1-111-1-1-1-11111-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-11111-1-1-1-1-111-1-11111
χ55111111111111111-1-1111-1-111-1-1-1-1-1-1-1-11111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111111111-1-1-1-1-1-1-111-1-11111-1-1
χ56111111111111111-1-1-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-11111-1-1-1-11111111-1-11111-1-1-1-1
χ57111111111111111-1-1-1-11-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-111111111-1-1-1-111111-1-1-1-1-1-111
χ5811111-1-11-11-111111-111-11-1-1-111-1-1ii−i−iii−i−i-1-11i−ii−ii−i1-1i−i-1-1-1-1-111-11-11-1-1-1-1-11-1-11-1111-1-111−i−iii−i−iii11-1−ii−ii−ii-11−ii
χ5911111-1-11-11-111111-111-11-1-1-111-1-1−i−iii−i−iii-1-11−ii−ii−ii1-1−ii-1-1-1-1-111-11-11-1-1-1-1-11-1-11-1111-1-111ii−i−iii−i−i11-1i−ii−ii−i-11i−i
χ6011111-1-11-11-111111-1-1-1-11-1-1-111-1-1ii−i−iii−i−i11-1i−ii−i−ii-11−ii-1-1-1-1-111-11-11-1-1-1-1-11111-1111-1-111−i−iii−i−iii-1-11−ii−iii−i1-1i−i
χ6111111-1-11-11-111111-1-1-1-11-1-1-111-1-1−i−iii−i−iii11-1−ii−iii−i-11i−i-1-1-1-1-111-11-11-1-1-1-1-11111-1111-1-111ii−i−iii−i−i-1-11i−ii−i−ii1-1−ii
χ6211111-1-11-11-11111-1111-1-11-1-1-1-111ii−i−i−i−iii-1-11i−i−iii−i-11−ii-1-1-1-1-111-11-11-1-1-1-11-1-1-111-11111-1-1−i−iiiii−i−i11-1−iii−i−ii1-1i−i
χ6311111-1-11-11-11111-1111-1-11-1-1-1-111−i−iiiii−i−i-1-11−iii−i−ii-11i−i-1-1-1-1-111-11-11-1-1-1-11-1-1-111-11111-1-1ii−i−i−i−iii11-1i−i−iii−i1-1−ii
χ6411111-1-11-11-11111-11-1-1-1-11-1-1-1-111ii−i−i−i−iii11-1i−i−ii−ii1-1i−i-1-1-1-1-111-11-11-1-1-1-11-11111-11111-1-1−i−iiiii−i−i-1-11−iii−ii−i-11−ii
χ6511111-1-11-11-11111-11-1-1-1-11-1-1-1-111−i−iiiii−i−i11-1−iii−ii−i1-1−ii-1-1-1-1-111-11-11-1-1-1-11-11111-11111-1-1ii−i−i−i−iii-1-11i−i−ii−ii-11i−i
χ662222222222222-2-22200-2222-2-2-2-2-2000000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2002-2-2-222222000000000000000000000
χ672222222222222-2-2-2-200-2-2-22-22222000000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2222200222-22-2-2-2-2000000000000000000000
χ6822222222222-2-22-20000200-2-2000022220000000-2-200000000-2-2-2-2-2-2-2-2-2-2-222-220000-200220000-2-2-2-200000002200000000
χ6922222222222-2-22-20000200-2-20000-2-2-2-200000002200000000-2-2-2-2-2-2-2-2-2-2-222-220000-20022000022220000000-2-200000000
χ7022222222222-2-2-220000-200-2200000000222200000-2-2000000-2-2-2-2-2-2-2-2-2-2-2222-200002002-200000000-2-2-2-20000022000000
χ7122222222222-2-2-220000-200-2200000000-2-2-2-20000022000000-2-2-2-2-2-2-2-2-2-2-2222-200002002-200000000222200000-2-2000000
χ7222222-2-22-22-222-2-22-20022-2-22-2-222000000000000000000000-2-2-2-2-222-22-22-2-222-2200-2-222-222-2-2000000000000000000000
χ7322222-2-22-22-222-2-2-22002-22-2222-2-2000000000000000000000-2-2-2-2-222-22-22-2-2222-200-22-22-2-2-222000000000000000000000
χ7422222-2-22-22-2-2-22-20000-2002200002i2i−2i−2i0000000−2i2i00000000-2-2-2-2-222-22-2222-220000200-2-20000−2i−2i2i2i00000002i−2i00000000
χ7522222-2-22-22-2-2-22-20000-200220000−2i−2i2i2i00000002i−2i00000000-2-2-2-2-222-22-2222-220000200-2-200002i2i−2i−2i0000000−2i2i00000000
χ7622222-2-22-22-2-2-2-2200002002-2000000002i2i−2i−2i00000−2i2i000000-2-2-2-2-222-22-22222-20000-200-2200000000−2i−2i2i2i000002i−2i000000
χ7722222-2-22-22-2-2-2-2200002002-200000000−2i−2i2i2i000002i−2i000000-2-2-2-2-222-22-22222-20000-200-22000000002i2i−2i−2i00000−2i2i000000
χ784444444-4-4-4-400000022000000000000000002-2-20000000000-4-4-4-4-4-4-44444000000-2-200000000000000000-2220000000000
χ794444444-4-4-4-4000000-2-200000000000000000-2220000000000-4-4-4-4-4-4-4444400000022000000000000000002-2-20000000000
χ8044444-4-4-44-440000002200000000000000000-22-20000000000-4-4-4-4-4444-44-4000000-2-2000000000000000002-220000000000
χ8144444-4-4-44-44000000-2-2000000000000000002-220000000000-4-4-4-4-4444-44-40000002200000000000000000-22-20000000000
χ82444-4-400040-400000000000002-22-22i−2i2i−2i2i−2i2i−2i0000000000000-4-4-444000-4040000000000000-22-22−2i2i−2i2i−2i2i−2i2i0000000000000
χ83444-4-400040-400000000000002-22-2−2i2i−2i2i−2i2i−2i2i0000000000000-4-4-444000-4040000000000000-22-222i−2i2i−2i2i−2i2i−2i0000000000000
χ84444-4-400040-40000000000000-22-222i−2i2i−2i−2i2i−2i2i0000000000000-4-4-444000-40400000000000002-22-2−2i2i−2i2i2i−2i2i−2i0000000000000
χ85444-4-400040-40000000000000-22-22−2i2i−2i2i2i−2i2i−2i0000000000000-4-4-444000-40400000000000002-22-22i−2i2i−2i−2i2i−2i2i0000000000000
χ86444-4-4000-40400000000000002-2-222-2-222-2-220000000000000-4-4-44400040-40000000000000-222-2-222-2-222-20000000000000
χ87444-4-4000-40400000000000002-2-22-222-2-222-20000000000000-4-4-44400040-40000000000000-222-22-2-222-2-220000000000000
χ88444-4-4000-4040000000000000-222-22-2-22-222-20000000000000-4-4-44400040-400000000000002-2-22-222-22-2-220000000000000
χ89444-4-4000-4040000000000000-222-2-222-22-2-220000000000000-4-4-44400040-400000000000002-2-222-2-22-222-20000000000000
χ9044-4-4400-40404-400040000-4000000000000000000000000000-4-444-40040-40-44000-400004000000000000000000000000000
χ9144-4-4400-40404-4000-400004000000000000000000000000000-4-444-40040-40-4400040000-4000000000000000000000000000
χ9244-4-4400-4040-440040000-40000000000000000000000000000-4-444-40040-404-400-4000040000000000000000000000000000
χ9344-4-4400-4040-4400-4000040000000000000000000000000000-4-444-40040-404-40040000-40000000000000000000000000000
χ9488-88-88-8000000000000000000000000000000000000000000-8-88-88-88000000000000000000000000000000000000000000
χ9588-88-8-88000000000000000000000000000000000000000000-8-88-888-8000000000000000000000000000000000000000000
χ9688-8-880080-8000000000000000000000000000000000000000-8-888-800-808000000000000000000000000000000000000000
χ9716-160000000000000004-4000000000000000000000000000000-1616000000000000000-44000000000000000000000000000000
χ9816-16000000000000000-44000000000000000000000000000000-16160000000000000004-4000000000000000000000000000000

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