Finite Group Databasebeta

← Group #72337577

Character table — Group #72337577

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size112224444448888881616161616161616161616161616161616323232323232323232323264646464646464646464646464128128128128
order12222222222222244222222244444444442444444444444444444444448888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-111-111-1-11111-1-1-1-111-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-111-111-1-1-1-1-1-11111-1-111
χ51111111111111111111111-1-1-1-111111111-1-11111111-1-1-1-1-1-1-1ii−i−iii−i−ii−ii−i
χ61111111111111111111111-1-1-1-111111111-1-11111111-1-1-1-1-1-1-1−i−iii−i−iii−ii−ii
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-11-1-111ii−i−i−i−iiii−i−ii
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-11-1-111−i−iiiii−i−i−iii−i
χ911111111111-1-1-1-111111-1-111111111-1-1-1-1111-1-1-1-111111-1-1-1-111111111-1-1-1-1
χ1011111111111-1-1-1-111111-1-111111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ1111111111111-1-1-1-111111-1-11111-1-1-1-11111-1-1111-1-1-1-111-1-1-1111111-1-1-1-1-1-111
χ1211111111111-1-1-1-111111-1-11111-1-1-1-11111-1-1111-1-1-1-111-1-1-111-1-1-1-1111111-1-1
χ1311111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-11-1-1-1-111-1-1-11111ii−i−iii−i−i−ii−ii
χ1411111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-11-1-1-1-111-1-1-11111−i−iii−i−iiii−ii−i
χ1511111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1111-1-1ii−i−i−i−iii−iii−i
χ1611111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1111-1-1−i−iiiii−i−ii−i−ii
χ17222222222220000222-2-20022222222000022-20000-2-2-2-2-20000000000000000
χ18222222222220000222-2-2002222-2-2-2-20000-2-2-2000022-2-220000000000000000
χ19222222222220000222-2-200-2-2-2-222220000-2-2-20000-2-22220000000000000000
χ20222222222220000222-2-200-2-2-2-2-2-2-2-2000022-200002222-20000000000000000
χ21222222222220000-2-2-2-2-2002-22-200002222002-2-200002-20002-2000000000000
χ22222222222220000-2-2-2-2-2002-22-20000-2-2-2-20022200002-2000-22000000000000
χ23222222222220000-2-2-2-2-200-22-2200002222002-2-20000-22000-22000000000000
χ24222222222220000-2-2-2-2-200-22-220000-2-2-2-2002220000-220002-2000000000000
χ25222222222222222-2-2-222222-22-20000000000-200-2-200-2202-200000000000000
χ26222222222222222-2-2-22222-22-220000000000-200-2-2002-20-2200000000000000
χ2722222222222-2-2-2-2-2-2-222-2-22-22-20000000000-2002200-220-2200000000000000
χ2822222222222-2-2-2-2-2-2-222-2-2-22-220000000000-20022002-202-200000000000000
χ29444444-4-44-4-400000000000040-400000000000000000000000000002-22-20000
χ30444444-4-44-4-400000000000040-40000000000000000000000000000-22-220000
χ31444444-4-44-4-4000000000000-40400000000000000000000000000002i−2i−2i2i0000
χ32444444-4-44-4-4000000000000-4040000000000000000000000000000−2i2i2i−2i0000
χ3344444-44-4-44-40000000000040-400000000000000000000000002-22-200000000
χ3444444-44-4-44-40000000000040-40000000000000000000000000-22-2200000000
χ3544444-44-4-44-400000000000-40400000000000000000000000002i−2i−2i2i00000000
χ3644444-44-4-44-400000000000-4040000000000000000000000000−2i2i2i−2i00000000
χ3744444-4-44-4-44000044-40000000044-4-400000000000000000000000000000000
χ3844444-4-44-4-44000044-400000000-4-44400000000000000000000000000000000
χ3944444-4-44-4-440000-4-44000000000000000000000004-40000000000000000000
χ4044444-4-44-4-440000-4-4400000000000000000000000-440000000000000000000
χ4144-4-4400-400422224-4000-2-20000004-422-2-20002-22-2000000000000000000000
χ4244-4-4400-400422224-4000-2-2000000-44-2-222000-222-2000000000000000000000
χ4344-4-4400-40042222-44000-2-200004-40022-2-2000-22-22000000000000000000000
χ4444-4-4400-40042222-44000-2-20000-4400-2-2220002-2-22000000000000000000000
χ4544-4-4400-4004-2-2-2-24-4000220000004-4-2-222000-22-22000000000000000000000
χ4644-4-4400-4004-2-2-2-24-400022000000-4422-2-20002-2-22000000000000000000000
χ4744-4-4400-4004-2-2-2-2-440002200004-400-2-2220002-22-2000000000000000000000
χ4844-4-4400-4004-2-2-2-2-44000220000-440022-2-2000-222-2000000000000000000000
χ49888-8-80800-8000000000000000000004i−4i4i−4i0000000000000000000000000000
χ50888-8-80800-800000000000000000000−4i4i−4i4i0000000000000000000000000000
χ51888-8-80-8008044-4-4000004-40000000000000000000000000000000000000000
χ52888-8-80-80080-4-44400000-440000000000000000000000000000000000000000
χ5388-88-8800-80000000000000000000004i−4i−4i4i0000000000000000000000000000
χ5488-88-8800-8000000000000000000000−4i4i4i−4i0000000000000000000000000000
χ5588-88-8-80080044-4-400000-440000000000000000000000000000000000000000
χ5688-88-8-800800-4-444000004-40000000000000000000000000000000000000000
χ5788-8-8800800-8000000000000000000000004-400000000000000000000000000
χ5888-8-8800800-800000000000000000000000-4400000000000000000000000000
χ5916-16000000000008-80004-4000000000000000000000000000000000000000000
χ6016-1600000000000-880004-4000000000000000000000000000000000000000000
χ6116-160000000008-800000-44000000000000000000000000000000000000000000
χ6216-16000000000-8800000-44000000000000000000000000000000000000000000

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