Finite Group Databasebeta

← Group #72323514

Character table — Group #72323514

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11222444444881616161616161616161616161616163232323232323232323232323232323232646464646464646464646464646464128128
order12222222222222222444444444442244444444444444444444444444444488
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11-11-111-1-1-1-1-1-1-1-1-1-1111-111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-11-11-111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-11-1-111111-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-11-1-11-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-1-1-1-1-1-11-111111-1-111-1-1111-1-1-11111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-1-11-111111-1-111-1-1111-1-1-1-1-1-1-111111111-1-1
χ911111111111-1-11-1-1-11-1-111111111-11-11111111-1-1-1-1-1-1-1-11-1ii−i−iii−i−iii−i−ii−i
χ1011111111111-1-11-1-1-11-1-111111111-11-11111111-1-1-1-1-1-1-1-11-1−i−iii−i−iii−i−iii−ii
χ1111111111111-1-11-1-1-11-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111ii−i−iii−i−i−i−iii−ii
χ1211111111111-1-11-1-1-11-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111−i−iii−i−iiiii−i−ii−i
χ1311111111111-1-11-1-1-11-1-1-1-1-1-111111-11-111-1-11111-1-111-11-1-1ii−i−i−i−iiiii−i−i−ii
χ1411111111111-1-11-1-1-11-1-1-1-1-1-111111-11-111-1-11111-1-111-11-1-1−i−iiiii−i−i−i−iiii−i
χ1511111111111-1-11-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-11-11ii−i−i−i−iii−i−iiii−i
χ1611111111111-1-11-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-11-11−i−iiiii−i−iii−i−i−ii
χ1722222222222222-22-2222000022220000-2-200-2-2002200-200-200000000000000
χ1822222222222222-22-22220000-2-2-2-20000-2-2002200-2-200-200200000000000000
χ192222222222222-22-22-22-22222000020202-20000000000-2-2-2000000000000000
χ202222222222222-22-22-22-2-2-2-2-20000-20-202-20000000000-222000000000000000
χ212222222222222-2-2-2-2-22-2000000000202-22-2-200-2-20022200000000000000000
χ222222222222222-2-2-2-2-22-2000000000-20-2-2222002200-2-2200000000000000000
χ2322222222222-2-222-222-2-2000022220000-2-200-2-200-2-200200200000000000000
χ2422222222222-2-222-222-2-20000-2-2-2-20000-2-20022002200200-200000000000000
χ2522222222222-2-2-2222-2-22000000000202-22-2-2002200-2-2-200000000000000000
χ2622222222222-2-2-2222-2-22000000000-20-2-222200-2-20022-200000000000000000
χ2722222222222-2-2-2-22-2-2-2222220000-20-202-2000000000022-2000000000000000
χ2822222222222-2-2-2-22-2-2-22-2-2-2-2000020202-200000000002-22000000000000000
χ29444444-4-4-4-444400000-4000000000000000000000000000002-22-20000000000
χ30444444-4-4-4-444400000-400000000000000000000000000000-22-220000000000
χ31444444-4-4-4-44-4-4000004000000000000000000000000000002i−2i−2i2i0000000000
χ32444444-4-4-4-44-4-400000400000000000000000000000000000−2i2i2i−2i0000000000
χ3344444-444-4-4-4004000-40000000000000000004i−4i000000000000000000000000
χ3444444-444-4-4-4004000-4000000000000000000−4i4i000000000000000000000000
χ3544444-444-4-4-400-400040000004i4i−4i−4i0000000000000000000000000000000000
χ3644444-444-4-4-400-40004000000−4i−4i4i4i0000000000000000000000000000000000
χ3744444-4-4-444-400004000-40000000000000000000000000000000000002-22-200
χ3844444-4-4-444-400004000-4000000000000000000000000000000000000-22-2200
χ3944444-4-4-444-40000-400040000000000000000000000000000000000002i−2i−2i2i00
χ4044444-4-4-444-40000-40004000000000000000000000000000000000000−2i2i2i−2i00
χ41444-4-4-4000044-4000000022-2-22-22-220-20002-2002-22-200000000000000000000
χ42444-4-4-4000044-4000000022-2-2-22-2220-2000-2200-22-2200000000000000000000
χ43444-4-4-4000044-40000000-2-2222-22-2-202000-2200-222-200000000000000000000
χ44444-4-4-4000044-40000000-2-222-22-22-2020002-2002-2-2200000000000000000000
χ45444-4-4-400004-44000000022-2-22-22-2-2020002-200-22-2200000000000000000000
χ46444-4-4-400004-44000000022-2-2-22-22-202000-22002-22-200000000000000000000
χ47444-4-4-400004-440000000-2-2222-22-220-2000-22002-2-2200000000000000000000
χ48444-4-4-400004-440000000-2-222-22-2220-20002-200-222-200000000000000000000
χ49888-8-880000-800000000000004i−4i−4i4i0000000000000000000000000000000000
χ50888-8-880000-80000000000000−4i4i4i−4i0000000000000000000000000000000000
χ5188-88-80008-8000000000000000000040-4000000000000000000000000000000
χ5288-88-80008-80000000000000000000-404000000000000000000000000000000
χ5388-88-8000-8800000000004-44-400000000000000000000000000000000000000
χ5488-88-8000-880000000000-44-4400000000000000000000000000000000000000
χ5588-8-8808-800000000000000000000000000000000004-4000000000000000000
χ5688-8-8808-80000000000000000000000000000000000-44000000000000000000
χ5788-8-880-880000000000004-4-4400000000000000000000000000000000000000
χ5888-8-880-88000000000000-444-400000000000000000000000000000000000000
χ5916-1600000000000040-4000000000000000000000000000000000002i−2i2i−2i000000
χ6016-1600000000000040-400000000000000000000000000000000000−2i2i−2i2i000000
χ6116-16000000000000-404000000000000000000000000000000000002-2-22000000
χ6216-16000000000000-40400000000000000000000000000000000000-222-2000000

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