Finite Group Databasebeta

← Group #72268230

Character table — Group #72268230

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112266668888242424242424242448484848484848484848484864646464646464649696128128128128128128128128128128128128
order122222222222442222444424444444444433666666446666666612121212
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ31111111111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ41111111111-1-1-1-11111111111-1-11111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1
χ51111111111-1-1-1-11111111111-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321+i321−i321−i32
χ61111111111-1-1-1-11111111111-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321−i321+i321+i32
χ7333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000003-1000000000000
χ833333333333333-1-1-1-13333-1-133-1-1-1-1-1-1-1-100000000-1-1000000000000
χ933333333333333-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-100000000-13000000000000
χ1033333333333333-1-1-1-1-1-1-1-1-1-1-1-133-1-133-1-100000000-1-1000000000000
χ1133333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-133-1-13300000000-1-1000000000000
χ123333333333-3-3-3-33333-1-1-1-1-1-111-1-1-1-1111100000000-31000000000000
χ133333333333-3-3-3-3-1-1-1-13333-1-1-3-3-1-1-1-111110000000011000000000000
χ143333333333-3-3-3-3-1-1-1-1-1-1-1-13311-1-1-1-11111000000001-3000000000000
χ153333333333-3-3-3-3-1-1-1-1-1-1-1-1-1-11133-1-1-3-3110000000011000000000000
χ163333333333-3-3-3-3-1-1-1-1-1-1-1-1-1-111-1-13311-3-30000000011000000000000
χ174444-4-44-4-4444-4-4000000000000000000001111111100-1-111-1-111-1-1-1-1
χ184444-4-44-4-4444-4-400000000000000000000−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32001+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i321−i321−i32
χ194444-4-44-4-4444-4-400000000000000000000−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32001−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i321+i321+i32
χ204444-4-44-4-44-4-444000000000000000000001111111100-1-1-1-1-1-1-1-11111
χ214444-4-44-4-44-4-44400000000000000000000−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32001+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ224444-4-44-4-44-4-44400000000000000000000−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32001−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ2344-4-44-4-44-444-44-40000000000000000000011-1-1-1-111001-11-11-11-11-11-1
χ2444-4-44-4-44-444-44-400000000000000000000−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i3200−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1+i321−i32
χ2544-4-44-4-44-444-44-400000000000000000000−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i3200−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1−i321+i32
χ2644-4-44-4-44-44-44-440000000000000000000011-1-1-1-111001-1-111-1-11-11-11
χ2744-4-44-4-44-44-44-4400000000000000000000−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i3200−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i321+i32−1−i321−i32−1+i32
χ2844-4-44-4-44-44-44-4400000000000000000000−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i3200−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i321−i32−1+i321+i32−1−i32
χ2944-4-4-44-4-4444-4-440000000000000000000011-1-1-1-11100-111-1-111-1-11-11
χ3044-4-4-44-4-4444-4-4400000000000000000000−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32001+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i321+i32−1−i321−i32−1+i32
χ3144-4-4-44-4-4444-4-4400000000000000000000−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32001−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i321−i32−1+i321+i32−1−i32
χ3244-4-4-44-4-444-444-40000000000000000000011-1-1-1-11100-11-11-11-111-11-1
χ3344-4-4-44-4-444-444-400000000000000000000−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32001+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32−1−i321+i32−1+i321−i32
χ3444-4-4-44-4-444-444-400000000000000000000−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32001−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32−1+i321−i32−1−i321+i32
χ35666666-2-2-2-2000022-2-26-2-2-22-2002-22-200000000000000000000000000
χ36666666-2-2-2-2000022-2-2-26-2-22-200-22-2200000000000000000000000000
χ37666666-2-2-2-2000022-2-2-2-26-2-22002-2-2200000000000000000000000000
χ38666666-2-2-2-2000022-2-2-2-2-26-2200-222-200000000000000000000000000
χ39666666-2-2-2-20000-2-2226-2-2-2-2200-22-2200000000000000000000000000
χ40666666-2-2-2-20000-2-222-26-2-2-22002-22-200000000000000000000000000
χ41666666-2-2-2-20000-2-222-2-26-22-200-222-200000000000000000000000000
χ42666666-2-2-2-20000-2-222-2-2-262-2002-2-2200000000000000000000000000
χ438-88-80000000000004-40000000000000000222-22-2-2-200000000000000
χ448-88-80000000000004-40000000000000000−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i300000000000000
χ458-88-80000000000004-40000000000000000−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i300000000000000
χ468-8-8800000000004-400000000000000000022-22-22-2-200000000000000
χ478-8-8800000000004-4000000000000000000−1−i3−1+i31+i3−1−i31−i3−1+i31+i31−i300000000000000
χ488-8-8800000000004-4000000000000000000−1+i3−1−i31−i3−1+i31+i3−1−i31−i31+i300000000000000
χ4912121212-12-12-444-4000000000000004-4000000000000000000000000000000
χ5012121212-12-12-444-400000000000000-44000000000000000000000000000000
χ511212-12-1212-124-44-400000000000000000000004i−4i0000000000000000000000
χ521212-12-1212-124-44-40000000000000000000000−4i4i0000000000000000000000
χ531212-12-12-121244-4-4000000000000000000004i−4i000000000000000000000000
χ541212-12-12-121244-4-400000000000000000000−4i4i000000000000000000000000
χ5524-2424-24000000000000-4400000000000000000000000000000000000000
χ5624-24-24240000000000-440000000000000000000000000000000000000000

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