Finite Group Databasebeta

← Group #13181077

Character table — Group #13181077

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1122222224444444444444444448888888888888888991212121212121212121212121818181818181824242424242424242424242436363636363672727272108108108108
order122344666333366666666661212121236666121212121212121212121222444412121212121212122446666121212121212121212121212224412126612128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111-1-111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11-11-1111-11-111-1-1
χ61111-1-111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-11-1111-11-11-1-111
χ71111-1-111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-11111111-11-1111-11-1-1-111
χ81111-1-111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-1111111-11-1111-11-1111-1-1
χ911-111-1-1-111111-1-1-1-1-1-111111-1111-1-1-11111-1-1-1-111-1-1-1-11-11-111-1-111-1-11-1111-1-1111-1-1-1111-1-1-11-1-111-11-1-111-11-1
χ1011-111-1-1-111111-1-1-1-1-1-111111-1111-1-1-11111-1-1-1-111-1-1-1-11-11-111-1-111-1-11-1111-1-1111-1-1-1111-1-1-1-111-11-1-111-1-11-11
χ1111-111-1-1-111111-1-1-1-1-1-111111-1111-1-1-11111-1-1-1-111-1-1-1-1-11-11-1-111-1-1111-1111-1-1-1-1-1111-1-1-11111-1-111-11-1-11-11-11
χ1211-111-1-1-111111-1-1-1-1-1-111111-1111-1-1-11111-1-1-1-111-1-1-1-1-11-11-1-111-1-1111-1111-1-1-1-1-1111-1-1-1111-111-11-1-111-11-11-1
χ1311-11-11-1-111111-1-1-1-1-1-11111-11-1-11-1-1-11-1-1-11111-1-111111-1-1111-1-1-1-111-1-11-1-111111-1-1-1-1-1-111111-1-11-111-1-11-1-11
χ1411-11-11-1-111111-1-1-1-1-1-11111-11-1-11-1-1-11-1-1-11111-1-111111-1-1111-1-1-1-111-1-11-1-111111-1-1-1-1-1-1111-1-1111-1-1-111-111-1
χ1511-11-11-1-111111-1-1-1-1-1-11111-11-1-11-1-1-11-1-1-11111-1-11111-111-1-1-11111-1-1-1-11-1-111-1-1-1111111-1-1-111-1-11-111-1-1-111-1
χ1611-11-11-1-111111-1-1-1-1-1-11111-11-1-11-1-1-11-1-1-11111-1-11111-111-1-1-11111-1-1-1-11-1-111-1-1-1111111-1-1-1-1-1111-1-1-1111-1-11
χ172222222222222222222222222222222222222222222-2-2000000000000-2-2-2-2-2-2-20000000000000000-2-200000000
χ182222-2-222222222222222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-2220000000000002-2-222220000000000000000-2-200000000
χ19222-122-1-1-12-1-1222-1-1-1-12-1-12-1-122-12-1-1-12-1-12-1-12-1-1-1-1222222-1-1-1-1-1-1-1-1222-1-1-1-12-1-12-1-12-1-12-1-10000-1-100000000
χ20222-122-1-1-12-1-1222-1-1-1-12-1-12-1-122-12-1-1-12-1-12-1-12-1-1-1-122-2-2-2-211111111222-1-1-1-1-211-211-211-2110000-1-100000000
χ21222-122-1-1-12-1-1222-1-1-1-12-1-12-1-122-12-1-1-12-1-12-1-12-1-1-1-1-2-20000−i3i3−i3i3−i3i3−i3i3-2-2-211110−i3i30−i3i30−i3i30−i3i300001100000000
χ22222-122-1-1-12-1-1222-1-1-1-12-1-12-1-122-12-1-1-12-1-12-1-12-1-1-1-1-2-20000i3−i3i3−i3i3−i3i3−i3-2-2-211110i3−i30i3−i30i3−i30i3−i300001100000000
χ23222-1-2-2-1-1-12-1-1222-1-1-1-12-1-1211-2-2-12-1-1-1-211-211-21111220000−i3i3−i3i3i3−i3i3−i32-2-2-1-1-1-10−i3i30−i3i30i3−i30i3−i300001100000000
χ24222-1-2-2-1-1-12-1-1222-1-1-1-12-1-1211-2-2-12-1-1-1-211-211-21111220000i3−i3i3−i3−i3i3−i3i32-2-2-1-1-1-10i3−i30i3−i30−i3i30−i3i300001100000000
χ25222-1-2-2-1-1-12-1-1222-1-1-1-12-1-1211-2-2-12-1-1-1-211-211-21111-2-222-2-2-1-1-1-11111-22211112-1-12-1-1-211-2110000-1-100000000
χ26222-1-2-2-1-1-12-1-1222-1-1-1-12-1-1211-2-2-12-1-1-1-211-211-21111-2-2-2-2221111-1-1-1-1-2221111-211-2112-1-12-1-10000-1-100000000
χ2722-222-2-2-222222-2-2-2-2-2-222222-2222-2-2-22222-2-2-2-222-2-222000000000000-22-2-2-2220000000000000000-2200000000
χ2822-22-22-2-222222-2-2-2-2-2-22222-22-2-22-2-2-22-2-2-22222-2-222-2-200000000000022-222-2-20000000000000000-2200000000
χ2922-2-12-211-12-1-12-2-211112-1-12-1122-1-211-12-1-1-211-2-1-111220000−i3i3i3−i3−i3i3i3−i3-22-211-1-10−i3i30i3−i30−i3i30i3−i300001-100000000
χ3022-2-12-211-12-1-12-2-211112-1-12-1122-1-211-12-1-1-211-2-1-111220000i3−i3−i3i3i3−i3−i3i3-22-211-1-10i3−i30−i3i30i3−i30−i3i300001-100000000
χ3122-2-12-211-12-1-12-2-211112-1-12-1122-1-211-12-1-1-211-2-1-111-2-22-22-2-1-111-1-1112-22-1-1112-1-1-2112-1-1-2110000-1100000000
χ3222-2-12-211-12-1-12-2-211112-1-12-1122-1-211-12-1-1-211-2-1-111-2-2-22-2211-1-111-1-12-22-1-111-2112-1-1-2112-1-10000-1100000000
χ3322-2-1-2211-12-1-12-2-211112-1-121-1-2-2-1-211-1-2112-1-1211-1-1222-2-22-1-11111-1-1-2-2211-1-12-1-1-211-2112-1-10000-1100000000
χ3422-2-1-2211-12-1-12-2-211112-1-121-1-2-2-1-211-1-2112-1-1211-1-122-222-211-1-1-1-111-2-2211-1-1-2112-1-12-1-1-2110000-1100000000
χ3522-2-1-2211-12-1-12-2-211112-1-121-1-2-2-1-211-1-2112-1-1211-1-1-2-20000−i3i3i3−i3i3−i3−i3i322-2-1-1110−i3i30i3−i30i3−i30−i3i300001-100000000
χ3622-2-1-2211-12-1-12-2-211112-1-121-1-2-2-1-211-1-2112-1-1211-1-1-2-20000i3−i3−i3i3−i3i3i3−i322-2-1-1110i3−i30−i3i30−i3i30i3−i300001-100000000
χ37444444444111-2111111111-244-2-2-2-2-2-2-2111111-2-2-2-2-2002222222222220000000-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ38444444444111-2111111111-244-2-2-2-2-2-2-2111111-2-2-2-2-200-2-2-2-2-2-2-2-2-2-2-2-2000000011111111111100000000000000
χ39444444444-2-2-21-2-2-2-2-2-2-2-2-21441111111-2-2-2-2-2-211111000000000000000000000000000000000222200-1-1-1-10000
χ40444444444-2-2-21-2-2-2-2-2-2-2-2-21441111111-2-2-2-2-2-211111000000000000000000000000000000000-2-2-2-20011110000
χ414444-4-4444111-2111111111-2-4-422-2-2-2-2-2-1-1-1-1-1-1222220022-2-22222-2-2-2-20000000-1-1-1-1-1-111111100000000000000
χ424444-4-4444111-2111111111-2-4-422-2-2-2-2-2-1-1-1-1-1-12222200-2-222-2-2-2-222220000000111111-1-1-1-1-1-100000000000000
χ434444-4-4444-2-2-21-2-2-2-2-2-2-2-2-21-4-4-1-111111222222-1-1-1-1-10000000000000000000000000000000002-22-200-11-110000
χ444444-4-4444-2-2-21-2-2-2-2-2-2-2-2-21-4-4-1-111111222222-1-1-1-1-1000000000000000000000000000000000-22-22001-11-10000
χ45444-244-2-2-21−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i321−1−3i32−1+3i32-2-2-2-2-21-21111−1−3i32−1+3i321−1−3i32−1+3i32-21111002222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i30000000-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i3200000000000000
χ46444-244-2-2-21−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i321−1−3i32−1+3i32-2-2-2-2-21-21111−1−3i32−1+3i321−1−3i32−1+3i32-2111100-2-2-2-21+i31−i31+i31−i31+i31−i31+i31−i300000001−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3200000000000000
χ47444-244-2-2-21−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i321−1+3i32−1−3i32-2-2-2-2-21-21111−1+3i32−1−3i321−1+3i32−1−3i32-21111002222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i30000000-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i3200000000000000
χ48444-244-2-2-21−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i321−1+3i32−1−3i32-2-2-2-2-21-21111−1+3i32−1−3i321−1+3i32−1−3i32-2111100-2-2-2-21−i31+i31−i31+i31−i31+i31−i31+i300000001−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3200000000000000
χ49444-2-4-4-2-2-21−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i321−1−3i32−1+3i32-222221-2111-11+3i321−3i32-11+3i321−3i322-1-1-1-10022-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i30000000-11+i321−i32-11+i321−i321−1−i32−1+i321−1−i32−1+i3200000000000000
χ50444-2-4-4-2-2-21−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i321−1−3i32−1+3i32-222221-2111-11+3i321−3i32-11+3i321−3i322-1-1-1-100-2-2221+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i300000001−1−i32−1+i321−1−i32−1+i32-11+i321−i32-11+i321−i3200000000000000
χ51444-2-4-4-2-2-21−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i321−1+3i32−1−3i32-222221-2111-11−3i321+3i32-11−3i321+3i322-1-1-1-10022-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i30000000-11−i321+i32-11−i321+i321−1+i32−1−i321−1+i32−1−i3200000000000000
χ52444-2-4-4-2-2-21−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i321−1+3i32−1−3i32-222221-2111-11−3i321+3i32-11−3i321+3i322-1-1-1-100-2-2221−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i300000001−1+i32−1−i321−1+i32−1−i32-11−i321+i32-11−i321+i3200000000000000
χ5344-444-4-4-44111-2-1-1-1-1-1-1111-24-4-2-2-2222-2111-1-1-12-2-222002-22-222-2-222-2-20000000-1-1-1111-1-1-111100000000000000
χ5444-444-4-4-44111-2-1-1-1-1-1-1111-24-4-2-2-2222-2111-1-1-12-2-22200-22-22-2-222-2-2220000000111-1-1-1111-1-1-100000000000000
χ5544-444-4-4-44-2-2-21222222-2-2-214-4111-1-1-11-2-2-2222-111-1-10000000000000000000000000000000002-2-2200-111-10000
χ5644-444-4-4-44-2-2-21222222-2-2-214-4111-1-1-11-2-2-2222-111-1-1000000000000000000000000000000000-222-2001-1-110000
χ5744-44-44-4-44111-2-1-1-1-1-1-1111-2-4422-2222-2-1-1-1111-222-2-2002-2-2222-2-2-2-2220000000-1-1-1111111-1-1-100000000000000
χ5844-44-44-4-44111-2-1-1-1-1-1-1111-2-4422-2222-2-1-1-1111-222-2-200-222-2-2-22222-2-20000000111-1-1-1-1-1-111100000000000000
χ5944-44-44-4-44-2-2-21222222-2-2-21-44-1-11-1-1-11222-2-2-21-1-11100000000000000000000000000000000022-2-200-1-1110000
χ6044-44-44-4-44-2-2-21222222-2-2-21-44-1-11-1-1-11222-2-2-21-1-111000000000000000000000000000000000-2-2220011-1-10000
χ6144-4-24-422-21−1−3i32−1+3i32-2-1-11+3i321+3i321−3i321−3i321−1−3i32−1+3i32-2-22-2-212-1-111−1−3i32−1+3i32-11+3i321−3i32211-1-1002-22-2−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i30000000-11+i321−i321−1−i32−1+i32-11+i321−i321−1−i32−1+i3200000000000000
χ6244-4-24-422-21−1−3i32−1+3i32-2-1-11+3i321+3i321−3i321−3i321−1−3i32−1+3i32-2-22-2-212-1-111−1−3i32−1+3i32-11+3i321−3i32211-1-100-22-221+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i300000001−1−i32−1+i32-11+i321−i321−1−i32−1+i32-11+i321−i3200000000000000
χ6344-4-24-422-21−1+3i32−1−3i32-2-1-11−3i321−3i321+3i321+3i321−1+3i32−1−3i32-2-22-2-212-1-111−1+3i32−1−3i32-11−3i321+3i32211-1-1002-22-2−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i30000000-11−i321+i321−1+i32−1−i32-11−i321+i321−1+i32−1−i3200000000000000
χ6444-4-24-422-21−1+3i32−1−3i32-2-1-11−3i321−3i321+3i321+3i321−1+3i32−1−3i32-2-22-2-212-1-111−1+3i32−1−3i32-11−3i321+3i32211-1-100-22-221−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i300000001−1+i32−1−i32-11−i321+i321−1+i32−1−i32-11−i321+i3200000000000000
χ6544-4-2-4422-21−1−3i32−1+3i32-2-1-11+3i321+3i321−3i321−3i321−1−3i32−1+3i32-22-22212-1-11-11+3i321−3i321−1−3i32−1+3i32-2-1-111002-2-22−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i30000000-11+i321−i321−1−i32−1+i321−1−i32−1+i32-11+i321−i3200000000000000
χ6644-4-2-4422-21−1−3i32−1+3i32-2-1-11+3i321+3i321−3i321−3i321−1−3i32−1+3i32-22-22212-1-11-11+3i321−3i321−1−3i32−1+3i32-2-1-11100-222-21+i31−i3−1−i3−1+i3−1−i3−1+i31+i31−i300000001−1−i32−1+i32-11+i321−i32-11+i321−i321−1−i32−1+i3200000000000000
χ6744-4-2-4422-21−1+3i32−1−3i32-2-1-11−3i321−3i321+3i321+3i321−1+3i32−1−3i32-22-22212-1-11-11−3i321+3i321−1+3i32−1−3i32-2-1-111002-2-22−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i30000000-11−i321+i321−1+i32−1−i321−1+i32−1−i32-11−i321+i3200000000000000
χ6844-4-2-4422-21−1+3i32−1−3i32-2-1-11−3i321−3i321+3i321+3i321−1+3i32−1−3i32-22-22212-1-11-11−3i321+3i321−1+3i32−1−3i32-2-1-11100-222-21−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i300000001−1+i32−1−i32-11−i321+i32-11−i321+i321−1+i32−1−i3200000000000000
χ694-4040000-44444000000-4-4-4-400004000-4000000000004-4000000000000000004-400000000000000000000000000
χ704-4040000-44444000000-4-4-4-400004000-400000000000-4400000000000000000-4400000000000000000000000000
χ714-40-200−2i32i324-2-2400−2i32i3−2i32i3-422-40000-20−2i32i32000000000004-4000000000000000−2i32i3-2200000000000000000000000000
χ724-40-200−2i32i324-2-2400−2i32i3−2i32i3-422-40000-20−2i32i3200000000000-440000000000000002i3−2i32-200000000000000000000000000
χ734-40-2002i3−2i324-2-24002i3−2i32i3−2i3-422-40000-202i3−2i32000000000004-40000000000000002i3−2i3-2200000000000000000000000000
χ744-40-2002i3−2i324-2-24002i3−2i32i3−2i3-422-40000-202i3−2i3200000000000-44000000000000000−2i32i32-200000000000000000000000000
χ75888-488-4-4-4-4222-4-42222-4222-4-422-12-1-1-1-422-4222-1-1-1-100000000000000000000000000000000000000000000000
χ76888-4-8-8-4-4-4-4222-4-42222-422244-2-2-12-1-1-14-2-24-2-2-2111100000000000000000000000000000000000000000000000
χ7788-8-48-844-4-422244-2-2-2-2-4222-4422-1-211-1-4224-2-2-2-1-11100000000000000000000000000000000000000000000000
χ7888-8-4-8844-4-422244-2-2-2-2-42224-4-2-2-1-211-14-2-2-422211-1-100000000000000000000000000000000000000000000000
χ798-8080000-8222-46-66-6-66-2-2-240000-400040000000000000000000000000000000000000000000000000000000000
χ808-8080000-8222-4-66-666-6-2-2-240000-400040000000000000000000000000000000000000000000000000000000000
χ818-8080000-8-4-4-42000000444-2006i−6i2000-200000006i−6i0000000000000000000000000000000000000000000000000
χ828-8080000-8-4-4-42000000444-200−6i6i2000-20000000−6i6i0000000000000000000000000000000000000000000000000
χ838-80-400−4i34i342−1−3i3−1+3i3-46-6−3−i33+i33−i3−3+i3-21+3i31−3i340000202i3−2i3-20000000000000000000000000000000000000000000000000000000000
χ848-80-400−4i34i342−1+3i3−1−3i3-4-663−i3−3+i3−3−i33+i3-21−3i31+3i340000202i3−2i3-20000000000000000000000000000000000000000000000000000000000
χ858-80-400−4i34i34-4222002i3−2i32i3−2i34-2-2-2006i−6i-10−i3i310000000−3i3i33−3300000000000000000000000000000000000000000000000
χ868-80-400−4i34i34-4222002i3−2i32i3−2i34-2-2-200−6i6i-10−i3i3100000003i−3i−333300000000000000000000000000000000000000000000000
χ878-80-4004i3−4i342−1−3i3−1+3i3-4-663+i3−3−i3−3+i33−i3-21+3i31−3i34000020−2i32i3-20000000000000000000000000000000000000000000000000000000000
χ888-80-4004i3−4i342−1+3i3−1−3i3-46-6−3+i33−i33+i3−3−i3-21−3i31+3i34000020−2i32i3-20000000000000000000000000000000000000000000000000000000000
χ898-80-4004i3−4i34-422200−2i32i3−2i32i34-2-2-2006i−6i-10i3−i310000000−3i3i−333300000000000000000000000000000000000000000000000
χ908-80-4004i3−4i34-422200−2i32i3−2i32i34-2-2-200−6i6i-10i3−i3100000003i−3i33−3300000000000000000000000000000000000000000000000

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