Finite Group Databasebeta

← Group #72271408

Character table — Group #72271408

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size112881216161616242432323232323248112881216161616242432323232323248112881216161616242432323232323248112881216161616242432323232323248
order122244336624666612128222244666624666612128222244666624666612128222244666624666612128
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321
χ3111111−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111111−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111111−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111111−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321
χ4111-1-111111111-11-1-1-1-1111-1-111111111-11-1-1-1-1111-1-111111111-11-1-1-1-1111-1-111111111-11-1-1-1-1
χ5111-1-11−1+i32−1−i32−1+i32−1−i3211−1+i321−i32−1−i321+i321−i321+i32-1111-1-11−1+i32−1−i32−1+i32−1−i3211−1+i321−i32−1−i321+i321−i321+i32-1111-1-11−1+i32−1−i32−1+i32−1−i3211−1+i321−i32−1−i321+i321−i321+i32-1111-1-11−1+i32−1−i32−1+i32−1−i3211−1+i321−i32−1−i321+i321−i321+i32-1
χ6111-1-11−1−i32−1+i32−1−i32−1+i3211−1−i321+i32−1+i321−i321+i321−i32-1111-1-11−1−i32−1+i32−1−i32−1+i3211−1−i321+i32−1+i321−i321+i321−i32-1111-1-11−1−i32−1+i32−1−i32−1+i3211−1−i321+i32−1+i321−i321+i321−i32-1111-1-11−1−i32−1+i32−1−i32−1+i3211−1−i321+i32−1+i321−i321+i321−i32-1
χ73333330000-1-1000000-13333330000-1-1000000-13333330000-1-1000000-13333330000-1-1000000-1
χ8333-3-330000-1-10000001333-3-330000-1-10000001333-3-330000-1-10000001333-3-330000-1-10000001
χ944-42-20111100-1-1-1-111044-42-20111100-1-1-1-111044-42-20111100-1-1-1-111044-42-20111100-1-1-1-1110
χ1044-42-20−1+i32−1−i32−1+i32−1−i32001−i321−i321+i321+i32−1+i32−1−i32044-42-20−1+i32−1−i32−1+i32−1−i32001−i321−i321+i321+i32−1+i32−1−i32044-42-20−1+i32−1−i32−1+i32−1−i32001−i321−i321+i321+i32−1+i32−1−i32044-42-20−1+i32−1−i32−1+i32−1−i32001−i321−i321+i321+i32−1+i32−1−i320
χ1144-42-20−1−i32−1+i32−1−i32−1+i32001+i321+i321−i321−i32−1−i32−1+i32044-42-20−1−i32−1+i32−1−i32−1+i32001+i321+i321−i321−i32−1−i32−1+i32044-42-20−1−i32−1+i32−1−i32−1+i32001+i321+i321−i321−i32−1−i32−1+i32044-42-20−1−i32−1+i32−1−i32−1+i32001+i321+i321−i321−i32−1−i32−1+i320
χ1244-4-220111100-11-11-1-1044-4-220111100-11-11-1-1044-4-220111100-11-11-1-1044-4-220111100-11-11-1-10
χ1344-4-220−1+i32−1−i32−1+i32−1−i32001−i32−1+i321+i32−1−i321−i321+i32044-4-220−1+i32−1−i32−1+i32−1−i32001−i32−1+i321+i32−1−i321−i321+i32044-4-220−1+i32−1−i32−1+i32−1−i32001−i32−1+i321+i32−1−i321−i321+i32044-4-220−1+i32−1−i32−1+i32−1−i32001−i32−1+i321+i32−1−i321−i321+i320
χ1444-4-220−1−i32−1+i32−1−i32−1+i32001+i32−1−i321−i32−1+i321+i321−i32044-4-220−1−i32−1+i32−1−i32−1+i32001+i32−1−i321−i32−1+i321+i321−i32044-4-220−1−i32−1+i32−1−i32−1+i32001+i32−1−i321−i32−1+i321+i321−i32044-4-220−1−i32−1+i32−1−i32−1+i32001+i32−1−i321−i32−1+i321+i321−i320
χ1566600-200002-2000000066600-200002-2000000066600-200002-2000000066600-200002-20000000
χ1666600-20000-22000000066600-20000-22000000066600-20000-22000000066600-20000-220000000
χ178-8000022-2-20000000008-8000022-2-20000000008-8000022-2-20000000008-8000022-2-2000000000
χ188-80000−1+i3−1−i31−i31+i30000000008-80000−1+i3−1−i31−i31+i30000000008-80000−1+i3−1−i31−i31+i30000000008-80000−1+i3−1−i31−i31+i3000000000
χ198-80000−1−i3−1+i31+i31−i30000000008-80000−1−i3−1+i31+i31−i30000000008-80000−1−i3−1+i31+i31−i30000000008-80000−1−i3−1+i31+i31−i3000000000
χ201111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ21111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321-1-1-1-1-1-11−i321+i321−i321+i32-1-11−i321−i321+i321+i321−i321+i32-1111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321-1-1-1-1-1-11−i321+i321−i321+i32-1-11−i321−i321+i321+i321−i321+i32-1
χ22111111−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-1-1-1-1-1-11+i321−i321+i321−i32-1-11+i321+i321−i321−i321+i321−i32-1111111−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-1-1-1-1-1-11+i321−i321+i321−i32-1-11+i321+i321−i321−i321+i321−i32-1
χ23111-1-111111111-11-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-11111111-1-111111111-11-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-11111
χ24111-1-11−1+i32−1−i32−1+i32−1−i3211−1+i321−i32−1−i321+i321−i321+i32-1-1-1-111-11−i321+i321−i321+i32-1-11−i32−1+i321+i32−1−i32−1+i32−1−i321111-1-11−1+i32−1−i32−1+i32−1−i3211−1+i321−i32−1−i321+i321−i321+i32-1-1-1-111-11−i321+i321−i321+i32-1-11−i32−1+i321+i32−1−i32−1+i32−1−i321
χ25111-1-11−1−i32−1+i32−1−i32−1+i3211−1−i321+i32−1+i321−i321+i321−i32-1-1-1-111-11+i321−i321+i321−i32-1-11+i32−1−i321−i32−1+i32−1−i32−1+i321111-1-11−1−i32−1+i32−1−i32−1+i3211−1−i321+i32−1+i321−i321+i321−i32-1-1-1-111-11+i321−i321+i321−i32-1-11+i32−1−i321−i32−1+i32−1−i32−1+i321
χ263333330000-1-1000000-1-3-3-3-3-3-300001100000013333330000-1-1000000-1-3-3-3-3-3-30000110000001
χ27333-3-330000-1-10000001-3-3-333-3000011000000-1333-3-330000-1-10000001-3-3-333-3000011000000-1
χ2844-42-20111100-1-1-1-1110-4-44-220-1-1-1-1001111-1-1044-42-20111100-1-1-1-1110-4-44-220-1-1-1-1001111-1-10
χ2944-42-20−1+i32−1−i32−1+i32−1−i32001−i321−i321+i321+i32−1+i32−1−i320-4-44-2201−i321+i321−i321+i3200−1+i32−1+i32−1−i32−1−i321−i321+i32044-42-20−1+i32−1−i32−1+i32−1−i32001−i321−i321+i321+i32−1+i32−1−i320-4-44-2201−i321+i321−i321+i3200−1+i32−1+i32−1−i32−1−i321−i321+i320
χ3044-42-20−1−i32−1+i32−1−i32−1+i32001+i321+i321−i321−i32−1−i32−1+i320-4-44-2201+i321−i321+i321−i3200−1−i32−1−i32−1+i32−1+i321+i321−i32044-42-20−1−i32−1+i32−1−i32−1+i32001+i321+i321−i321−i32−1−i32−1+i320-4-44-2201+i321−i321+i321−i3200−1−i32−1−i32−1+i32−1+i321+i321−i320
χ3144-4-220111100-11-11-1-10-4-442-20-1-1-1-1001-11-111044-4-220111100-11-11-1-10-4-442-20-1-1-1-1001-11-1110
χ3244-4-220−1+i32−1−i32−1+i32−1−i32001−i32−1+i321+i32−1−i321−i321+i320-4-442-201−i321+i321−i321+i3200−1+i321−i32−1−i321+i32−1+i32−1−i32044-4-220−1+i32−1−i32−1+i32−1−i32001−i32−1+i321+i32−1−i321−i321+i320-4-442-201−i321+i321−i321+i3200−1+i321−i32−1−i321+i32−1+i32−1−i320
χ3344-4-220−1−i32−1+i32−1−i32−1+i32001+i32−1−i321−i32−1+i321+i321−i320-4-442-201+i321−i321+i321−i3200−1−i321+i32−1+i321−i32−1−i32−1+i32044-4-220−1−i32−1+i32−1−i32−1+i32001+i32−1−i321−i32−1+i321+i321−i320-4-442-201+i321−i321+i321−i3200−1−i321+i32−1+i321−i32−1−i32−1+i320
χ3466600-200002-20000000-6-6-60020000-22000000066600-200002-20000000-6-6-60020000-220000000
χ3566600-20000-220000000-6-6-600200002-2000000066600-20000-220000000-6-6-600200002-20000000
χ368-8000022-2-2000000000-880000-2-2220000000008-8000022-2-2000000000-880000-2-222000000000
χ378-80000−1+i3−1−i31−i31+i3000000000-8800001−i31+i3−1+i3−1−i30000000008-80000−1+i3−1−i31−i31+i3000000000-8800001−i31+i3−1+i3−1−i3000000000
χ388-80000−1−i3−1+i31+i31−i3000000000-8800001+i31−i3−1−i3−1+i30000000008-80000−1−i3−1+i31+i31−i3000000000-8800001+i31−i3−1−i3−1+i3000000000
χ3911111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ40111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321-1-1-1-1-1-11−i321+i321−i321+i32-1-11−i321−i321+i321+i321−i321+i32-1-1-1-1-1-1-11−i321+i321−i321+i32-1-11−i321−i321+i321+i321−i321+i32-1
χ41111111−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111111−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-1-1-1-1-1-11+i321−i321+i321−i32-1-11+i321+i321−i321−i321+i321−i32-1-1-1-1-1-1-11+i321−i321+i321−i32-1-11+i321+i321−i321−i321+i321−i32-1
χ42111-1-111111111-11-1-1-1-1111-1-111111111-11-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-11111-1-1-111-1-1-1-1-1-1-1-11-11111
χ43111-1-11−1+i32−1−i32−1+i32−1−i3211−1+i321−i32−1−i321+i321−i321+i32-1111-1-11−1+i32−1−i32−1+i32−1−i3211−1+i321−i32−1−i321+i321−i321+i32-1-1-1-111-11−i321+i321−i321+i32-1-11−i32−1+i321+i32−1−i32−1+i32−1−i321-1-1-111-11−i321+i321−i321+i32-1-11−i32−1+i321+i32−1−i32−1+i32−1−i321
χ44111-1-11−1−i32−1+i32−1−i32−1+i3211−1−i321+i32−1+i321−i321+i321−i32-1111-1-11−1−i32−1+i32−1−i32−1+i3211−1−i321+i32−1+i321−i321+i321−i32-1-1-1-111-11+i321−i321+i321−i32-1-11+i32−1−i321−i32−1+i32−1−i32−1+i321-1-1-111-11+i321−i321+i321−i32-1-11+i32−1−i321−i32−1+i32−1−i32−1+i321
χ453333330000-1-1000000-13333330000-1-1000000-1-3-3-3-3-3-30000110000001-3-3-3-3-3-30000110000001
χ46333-3-330000-1-10000001333-3-330000-1-10000001-3-3-333-3000011000000-1-3-3-333-3000011000000-1
χ4744-42-20111100-1-1-1-111044-42-20111100-1-1-1-1110-4-44-220-1-1-1-1001111-1-10-4-44-220-1-1-1-1001111-1-10
χ4844-42-20−1+i32−1−i32−1+i32−1−i32001−i321−i321+i321+i32−1+i32−1−i32044-42-20−1+i32−1−i32−1+i32−1−i32001−i321−i321+i321+i32−1+i32−1−i320-4-44-2201−i321+i321−i321+i3200−1+i32−1+i32−1−i32−1−i321−i321+i320-4-44-2201−i321+i321−i321+i3200−1+i32−1+i32−1−i32−1−i321−i321+i320
χ4944-42-20−1−i32−1+i32−1−i32−1+i32001+i321+i321−i321−i32−1−i32−1+i32044-42-20−1−i32−1+i32−1−i32−1+i32001+i321+i321−i321−i32−1−i32−1+i320-4-44-2201+i321−i321+i321−i3200−1−i32−1−i32−1+i32−1+i321+i321−i320-4-44-2201+i321−i321+i321−i3200−1−i32−1−i32−1+i32−1+i321+i321−i320
χ5044-4-220111100-11-11-1-1044-4-220111100-11-11-1-10-4-442-20-1-1-1-1001-11-1110-4-442-20-1-1-1-1001-11-1110
χ5144-4-220−1+i32−1−i32−1+i32−1−i32001−i32−1+i321+i32−1−i321−i321+i32044-4-220−1+i32−1−i32−1+i32−1−i32001−i32−1+i321+i32−1−i321−i321+i320-4-442-201−i321+i321−i321+i3200−1+i321−i32−1−i321+i32−1+i32−1−i320-4-442-201−i321+i321−i321+i3200−1+i321−i32−1−i321+i32−1+i32−1−i320
χ5244-4-220−1−i32−1+i32−1−i32−1+i32001+i32−1−i321−i32−1+i321+i321−i32044-4-220−1−i32−1+i32−1−i32−1+i32001+i32−1−i321−i32−1+i321+i321−i320-4-442-201+i321−i321+i321−i3200−1−i321+i32−1+i321−i32−1−i32−1+i320-4-442-201+i321−i321+i321−i3200−1−i321+i32−1+i321−i32−1−i32−1+i320
χ5366600-200002-2000000066600-200002-20000000-6-6-60020000-220000000-6-6-60020000-220000000
χ5466600-20000-22000000066600-20000-220000000-6-6-600200002-20000000-6-6-600200002-20000000
χ558-8000022-2-20000000008-8000022-2-2000000000-880000-2-222000000000-880000-2-222000000000
χ568-80000−1+i3−1−i31−i31+i30000000008-80000−1+i3−1−i31−i31+i3000000000-8800001−i31+i3−1+i3−1−i3000000000-8800001−i31+i3−1+i3−1−i3000000000
χ578-80000−1−i3−1+i31+i31−i30000000008-80000−1−i3−1+i31+i31−i3000000000-8800001+i31−i3−1−i3−1+i3000000000-8800001+i31−i3−1−i3−1+i3000000000
χ581111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111
χ59111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321-1-1-1-1-1-11−i321+i321−i321+i32-1-11−i321−i321+i321+i321−i321+i32-1-1-1-1-1-1-11−i321+i321−i321+i32-1-11−i321−i321+i321+i321−i321+i32-1111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321
χ60111111−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-1-1-1-1-1-11+i321−i321+i321−i32-1-11+i321+i321−i321−i321+i321−i32-1-1-1-1-1-1-11+i321−i321+i321−i32-1-11+i321+i321−i321−i321+i321−i32-1111111−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321
χ61111-1-111111111-11-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-11111-1-1-111-1-1-1-1-1-1-1-11-11111111-1-111111111-11-1-1-1-1
χ62111-1-11−1+i32−1−i32−1+i32−1−i3211−1+i321−i32−1−i321+i321−i321+i32-1-1-1-111-11−i321+i321−i321+i32-1-11−i32−1+i321+i32−1−i32−1+i32−1−i321-1-1-111-11−i321+i321−i321+i32-1-11−i32−1+i321+i32−1−i32−1+i32−1−i321111-1-11−1+i32−1−i32−1+i32−1−i3211−1+i321−i32−1−i321+i321−i321+i32-1
χ63111-1-11−1−i32−1+i32−1−i32−1+i3211−1−i321+i32−1+i321−i321+i321−i32-1-1-1-111-11+i321−i321+i321−i32-1-11+i32−1−i321−i32−1+i32−1−i32−1+i321-1-1-111-11+i321−i321+i321−i32-1-11+i32−1−i321−i32−1+i32−1−i32−1+i321111-1-11−1−i32−1+i32−1−i32−1+i3211−1−i321+i32−1+i321−i321+i321−i32-1
χ643333330000-1-1000000-1-3-3-3-3-3-30000110000001-3-3-3-3-3-300001100000013333330000-1-1000000-1
χ65333-3-330000-1-10000001-3-3-333-3000011000000-1-3-3-333-3000011000000-1333-3-330000-1-10000001
χ6644-42-20111100-1-1-1-1110-4-44-220-1-1-1-1001111-1-10-4-44-220-1-1-1-1001111-1-1044-42-20111100-1-1-1-1110
χ6744-42-20−1+i32−1−i32−1+i32−1−i32001−i321−i321+i321+i32−1+i32−1−i320-4-44-2201−i321+i321−i321+i3200−1+i32−1+i32−1−i32−1−i321−i321+i320-4-44-2201−i321+i321−i321+i3200−1+i32−1+i32−1−i32−1−i321−i321+i32044-42-20−1+i32−1−i32−1+i32−1−i32001−i321−i321+i321+i32−1+i32−1−i320
χ6844-42-20−1−i32−1+i32−1−i32−1+i32001+i321+i321−i321−i32−1−i32−1+i320-4-44-2201+i321−i321+i321−i3200−1−i32−1−i32−1+i32−1+i321+i321−i320-4-44-2201+i321−i321+i321−i3200−1−i32−1−i32−1+i32−1+i321+i321−i32044-42-20−1−i32−1+i32−1−i32−1+i32001+i321+i321−i321−i32−1−i32−1+i320
χ6944-4-220111100-11-11-1-10-4-442-20-1-1-1-1001-11-1110-4-442-20-1-1-1-1001-11-111044-4-220111100-11-11-1-10
χ7044-4-220−1+i32−1−i32−1+i32−1−i32001−i32−1+i321+i32−1−i321−i321+i320-4-442-201−i321+i321−i321+i3200−1+i321−i32−1−i321+i32−1+i32−1−i320-4-442-201−i321+i321−i321+i3200−1+i321−i32−1−i321+i32−1+i32−1−i32044-4-220−1+i32−1−i32−1+i32−1−i32001−i32−1+i321+i32−1−i321−i321+i320
χ7144-4-220−1−i32−1+i32−1−i32−1+i32001+i32−1−i321−i32−1+i321+i321−i320-4-442-201+i321−i321+i321−i3200−1−i321+i32−1+i321−i32−1−i32−1+i320-4-442-201+i321−i321+i321−i3200−1−i321+i32−1+i321−i32−1−i32−1+i32044-4-220−1−i32−1+i32−1−i32−1+i32001+i32−1−i321−i32−1+i321+i321−i320
χ7266600-200002-20000000-6-6-60020000-220000000-6-6-60020000-22000000066600-200002-20000000
χ7366600-20000-220000000-6-6-600200002-20000000-6-6-600200002-2000000066600-20000-220000000
χ748-8000022-2-2000000000-880000-2-222000000000-880000-2-2220000000008-8000022-2-2000000000
χ758-80000−1+i3−1−i31−i31+i3000000000-8800001−i31+i3−1+i3−1−i3000000000-8800001−i31+i3−1+i3−1−i30000000008-80000−1+i3−1−i31−i31+i3000000000
χ768-80000−1−i3−1+i31+i31−i3000000000-8800001+i31−i3−1−i3−1+i3000000000-8800001+i31−i3−1−i3−1+i30000000008-80000−1−i3−1+i31+i31−i3000000000

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