Finite Group Databasebeta

← Group #72344172

Character table — Group #72344172

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size1133441212121224242424323248484848484848484848969696969696128128128128128128128128192192192192
order12222244442244222244448888448888366666664488
χ111111111111111111111111111111111111111111111
χ21111111111111111-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1
χ311111111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1
χ411111111111111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-111
χ522222222222222220022000000002200-1-1-1-1-1-1-1-10000
χ622222222222222-2-2002200000000-2-200-1-1-1-111110000
χ72222-2-22-2-2222-2-200002-200000000000022-2-200000000
χ82222-2-22-2-2222-2-200002-2000000000000-1-111−i3−i3i3i30000
χ92222-2-22-2-2222-2-200002-2000000000000-1-111i3i3−i3−i30000
χ103333333333-1-1-1-13311-1-111111111-1-11100000000-1-1-1-1
χ113333333333-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000001111
χ123333333333-1-1-1-1-3-311-1-111-1-1-1-1-1-1111100000000-1-111
χ133333333333-1-1-1-1-3-3-1-1-1-1-1-111111111-1-10000000011-1-1
χ144-4-44-44000000002-22-2002-222-2-20000001-11-11-11-10000
χ154-4-44-44000000002-2-2200-22-2-2220000001-11-11-11-10000
χ164-4-44-4400000000-222-2002-2-2-2220000001-11-1-11-110000
χ174-4-44-4400000000-22-2200-2222-2-20000001-11-1-11-110000
χ18666666-2-2-2-222-2-20022-222200000000-2-2000000000000
χ19666666-2-2-2-222-2-200-2-2-22-2-20000000022000000000000
χ20666666-2-2-2-2-2-22200002-2002222-2-20000000000000000
χ21666666-2-2-2-2-2-22200002-200-2-2-2-2220000000000000000
χ226666-6-66-6-66-2-2220000-22000000000000000000000000
χ236666-6-6-222-222220000-2-2000000000000000000002-200
χ246666-6-6-222-222220000-2-200000000000000000000-2200
χ256666-6-6-222-2-2-2-2-200002200000000000000000000002i−2i
χ266666-6-6-222-2-2-2-2-20000220000000000000000000000−2i2i
χ278-8-888-8000000000000000000000000002-2-2200000000
χ288-8-888-800000000000000000000000000-111-1−i3i3i3−i30000
χ298-8-888-800000000000000000000000000-111-1i3−i3−i3i30000
χ308-8-88-88000000004-40000000000000000-11-11-11-110000
χ318-8-88-8800000000-440000000000000000-11-111-11-10000
χ321212-4-4000-4400000002200-2-22-22-2002-200000000000000
χ331212-4-4000-4400000002200-2-2-22-2200-2200000000000000
χ341212-4-4000-440000000-2-200222-22-200-2200000000000000
χ351212-4-4000-440000000-2-20022-22-22002-200000000000000
χ3612-124-400400-4004i−4i002-200-22000000002i−2i000000000000
χ3712-124-400400-4004i−4i00-22002-200000000−2i2i000000000000
χ3812-124-400400-400−4i4i002-200-2200000000−2i2i000000000000
χ3912-124-400400-400−4i4i00-22002-2000000002i−2i000000000000
χ4012-124-400-40044-400000000002-2-222-20000000000000000
χ4112-124-400-40044-40000000000-222-2-220000000000000000
χ4212-124-400-4004-4400000000002-2-22-220000000000000000
χ4312-124-400-4004-440000000000-222-22-20000000000000000
χ442424-8-80008-800000000000000000000000000000000000

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