Finite Group Databasebeta

← Group #72310520

Character table — Group #72310520

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11222444444881616161616161616161616161616161616161632323232323232323232326464646464646464646464646464646464128128
order12222222222442222222444444444444444444444444444444444444444488
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-11-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111-1-1-1-111-1-11111111111-1-1111111-1-1-1-1-1-1iiii−i−i−i−iii−i−ii−i
χ61111111111111111-1-1-1-111-1-11111111111-1-1111111-1-1-1-1-1-1−i−i−i−iiiii−i−iii−ii
χ71111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-111-111iiii−i−i−i−i−i−iii−ii
χ81111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-111-111−i−i−i−iiiiiii−i−ii−i
χ911111111111111-1-11111-1-1111111-1-1-1-111-1-111-1-1-1-111-1-11-111-1-111-1-11111-1-1
χ1011111111111111-1-11111-1-1111111-1-1-1-111-1-111-1-1-1-111-1-11-1-1-111-1-111-1-1-1-111
χ1111111111111111-1-11111-1-111-1-1-1-1111111-1-1-1-111-1-11-11-1-1111-1-111-1-1-1-1-1-111
χ1211111111111111-1-11111-1-111-1-1-1-1111111-1-1-1-111-1-11-11-1-11-1-111-1-1111111-1-1
χ1311111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-11ii−i−i−i−iiiii−i−i−ii
χ1411111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-11−i−iiiii−i−i−i−iiii−i
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-11-111-1ii−i−i−i−iii−i−iiii−i
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-11-111-1−i−iiiii−i−iii−i−i−ii
χ17222222222222222222-2-222-2-200000000-2-2-2-20000-2-220020000000000000000
χ182222222222222222-2-222222200000000-2-2220000-2-2-200-20000000000000000
χ1922222222222222-2-222-2-2-2-2-2-200000000-2-222000022200-20000000000000000
χ2022222222222222-2-2-2-222-2-22200000000-2-2-2-2000022-20020000000000000000
χ2122222222222-2-2-200222-2002-2000022222-20000-2-200-20200-200000000000000
χ2222222222222-2-2-200222-2002-20000-2-2-2-22-200002200-20-200200000000000000
χ2322222222222-2-2-20022-2200-2222220000-2200-2-20000-2200-2000000000000000
χ2422222222222-2-2-20022-2200-22-2-2-2-20000-2200220000-2-2002000000000000000
χ2522222222222-2-2-200-2-22-2002-222220000-2200-2-200002-2002000000000000000
χ2622222222222-2-2-200-2-22-2002-2-2-2-2-20000-22002200002200-2000000000000000
χ2722222222222-2-2-200-2-2-2200-22000022222-20000-2-20020-200200000000000000
χ2822222222222-2-2-200-2-2-2200-220000-2-2-2-22-20000220020200-200000000000000
χ29444444-4-44-4-4000000004000-40000000000000000000000002-2002-200000000
χ30444444-4-44-4-4000000004000-4000000000000000000000000-2200-2200000000
χ31444444-4-44-4-400000000-400040000000000000000000000002i−2i00−2i2i00000000
χ32444444-4-44-4-400000000-40004000000000000000000000000−2i2i002i−2i00000000
χ3344444-44-4-44-400000004000-40000000000000000000000000002-2002-2000000
χ3444444-44-4-44-400000004000-4000000000000000000000000000-2200-22000000
χ3544444-44-4-44-40000000-400040000000000000000000000000002i−2i00−2i2i000000
χ3644444-44-4-44-40000000-40004000000000000000000000000000−2i2i002i−2i000000
χ3744444-4-44-4-4444-44-400004-40000000000000000000000000000000000000000
χ3844444-4-44-4-4444-4-440000-440000000000000000000000000000000000000000
χ3944444-4-44-4-44-4-44000000000000000000000000004-400000000000000000000
χ4044444-4-44-4-44-4-4400000000000000000000000000-4400000000000000000000
χ41444-4-400400-44-400400000-4002i2i−2i−2i2i2i−2i−2i00002i−2i2i−2i0000000000000000000000
χ42444-4-400400-44-400400000-400−2i−2i2i2i−2i−2i2i2i0000−2i2i−2i2i0000000000000000000000
χ43444-4-400400-44-400-4000004002i2i−2i−2i−2i−2i2i2i00002i−2i−2i2i0000000000000000000000
χ44444-4-400400-44-400-400000400−2i−2i2i2i2i2i−2i−2i0000−2i2i2i−2i0000000000000000000000
χ45444-4-400400-4-440400000-40002i2i−2i−2i2i2i−2i−2i0000−2i2i−2i2i0000000000000000000000
χ46444-4-400400-4-440400000-4000−2i−2i2i2i−2i−2i2i2i00002i−2i2i−2i0000000000000000000000
χ47444-4-400400-4-440-40000040002i2i−2i−2i−2i−2i2i2i0000−2i2i2i−2i0000000000000000000000
χ48444-4-400400-4-440-4000004000−2i−2i2i2i2i2i−2i−2i00002i−2i−2i2i0000000000000000000000
χ49888-8-800-8008000000000000000000000004-400000000000000000000000000
χ50888-8-800-800800000000000000000000000-4400000000000000000000000000
χ5188-88-80800-8000000000000004i−4i4i−4i0000000000000000000000000000000000
χ5288-88-80800-800000000000000−4i4i−4i4i0000000000000000000000000000000000
χ5388-88-80-80080000000000000000004-44-4000000000000000000000000000000
χ5488-88-80-8008000000000000000000-44-44000000000000000000000000000000
χ5588-8-88800-800000000000000000004i−4i−4i4i000000000000000000000000000000
χ5688-8-88800-80000000000000000000−4i4i4i−4i000000000000000000000000000000
χ5788-8-88-80080000000000000004-4-440000000000000000000000000000000000
χ5888-8-88-8008000000000000000-444-40000000000000000000000000000000000
χ5916-16000000000000004-4000000000000000000000000000000000000002i−2i2i−2i00
χ6016-16000000000000004-400000000000000000000000000000000000000−2i2i−2i2i00
χ6116-1600000000000000-44000000000000000000000000000000000000002-2-2200
χ6216-1600000000000000-4400000000000000000000000000000000000000-222-200

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