Finite Group Databasebeta

← Group #72231563

Character table — Group #72231563

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size11222222244444444444444444444444488888888888888888888881616161616161616161616161616161616162424242424242424242424242424242432323232323296969696
order12222366622222222222244666666666622244444666666666666121224446661212121212121212121212222244444444444444121212124488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-11-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111-1-1-1-111111111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111-1-1-1-111111111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ71111111111111-1-1-1-111111111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1-1-11-1-1-1-1-1-111-1-111-1-11111-1-1-1-1111111-1-111
χ81111111111111-1-1-1-111111111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111111111-1-1
χ9111111111-1-1-1-111-1-11111111-1-1-1-111111-11-1-111-1-111-1-11111-1-1-1-11111-1-1-111-1-1-1-1-11111-1-11-11-11-11-111-1-111-1-11-111-1-11-11-1
χ10111111111-1-1-1-111-1-11111111-1-1-1-111111-11-1-111-1-111-1-11111-1-1-1-11111-1-1-111-1-1-1-1-11111-1-1-11-11-11-11-1-111-1-1111-111-1-1-11-11
χ11111111111-1-1-1-111-1-11111111-1-1-1-111111-11-1-111-1-111-1-11111-1-1-1-111-1-111-1-1-11111-1-1-111-1-11-11-11-11-111-1-111-1-1-11-1-111-11-11
χ12111111111-1-1-1-111-1-11111111-1-1-1-111111-11-1-111-1-111-1-11111-1-1-1-111-1-111-1-1-11111-1-1-111-1-1-11-11-11-11-1-111-1-111-11-1-1111-11-1
χ13111111111-1-1-1-1-1-1111111111-1-1-1-111111-1-11-1-1-11111-1-1-1-1-1-111111111-1-1-111-1-1-1-1-111-1-1111-1-111-1-1111-1-1-1-111-11-1-1111-1-11
χ14111111111-1-1-1-1-1-1111111111-1-1-1-111111-1-11-1-1-11111-1-1-1-1-1-111111111-1-1-111-1-1-1-1-111-1-111-111-1-111-1-1-11111-1-1-11-1-111-111-1
χ15111111111-1-1-1-1-1-1111111111-1-1-1-111111-1-11-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-11111-1-1-1-1-1111-1-111-1-1111-1-1-1-1111-111-1-1-111-1
χ16111111111-1-1-1-1-1-1111111111-1-1-1-111111-1-11-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-11111-1-1-1-1-111-111-1-111-1-1-11111-1-11-111-1-11-1-11
χ172222222222222222222-2-2-2-22222222222-222-2-2-2-2-2-2-22222222222-2-20000-2000000-200-2-2-2-200000000000000000000000000
χ182222222222222-2-2-2-222-2-2-2-22222222222-2-2-2-22222-2-222-2-2-2-2-2-2-2-2-2-20000-2000000-200222200000000000000000000000000
χ1922222222222-2-20000-2-222-2-222222-2-2-2-22200-2000022-2-200000000-2-200002000000-20000002-2002-200-2-22200000000000000
χ2022222222222-2-20000-2-222-2-222222-2-2-2-22200-2000022-2-200000000-2-200002000000-2000000-2200-220022-2-200000000000000
χ2122222222222-2-20000-2-2-2-22222222-2-2-2-22-20020000-2-2-2-200000000220000-20000002000000002-2002-20000-2-2220000000000
χ2222222222222-2-20000-2-2-2-22222222-2-2-2-22-20020000-2-2-2-200000000220000-2000000200000000-2200-22000022-2-20000000000
χ23222222222-2-2220000-2-222-2-22-2-2-2-2-2-2-2-22-20020000222200000000-2-20000-2000000200000022002200-2-2-2-200000000000000
χ24222222222-2-2220000-2-222-2-22-2-2-2-2-2-2-2-22-20020000222200000000-2-20000-20000002000000-2-200-2-200222200000000000000
χ25222222222-2-2220000-2-2-2-2222-2-2-2-2-2-2-2-22200-20000-2-222000000002200002000000-2000000002200220000-2-2-2-20000000000
χ26222222222-2-2220000-2-2-2-2222-2-2-2-2-2-2-2-22200-20000-2-222000000002200002000000-200000000-2-200-2-2000022220000000000
χ27222222222-2-2-2-222-2-222-2-2-2-22-2-2-2-22222222-22-2-222-2-2-2-22222-2-2-2-2-2-200002000000200-2-22200000000000000000000000000
χ28222222222-2-2-2-2-2-22222-2-2-2-22-2-2-2-2222222-22222-2-2-2-2-2-2-2-2-2-22222-2-20000200000020022-2-200000000000000000000000000
χ2922222-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ3022222-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1111111-111-1-1-1-10000000000000000-2-211110000
χ3122222-1-1-1-12222222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-222-2-2-2-2-211-1-1-1-1-1-1-1-1-1-11100001i3−i3i3i3−i3−i31i3−i31111000000000000000000i3−i3i3−i30000
χ3222222-1-1-1-12222222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-222-2-2-2-2-211-1-1-1-1-1-1-1-1-1-11100001−i3i3−i3−i3i3i31−i3i31111000000000000000000−i3i3−i3i30000
χ3322222-1-1-1-12222-2-2-2-2222222-1-1-1-1-1-1-1-1-1-12-2-22-2-2-2-2-1-1-1-111111111-1-12222-1-1-1-1-1-1-1-1-1-111110000000000000000-2-211110000
χ3422222-1-1-1-12222-2-2-2-2222222-1-1-1-1-1-1-1-1-1-12-2-22-2-2-2-2-1-1-1-111111111-1-1-2-2-2-2-1111111-1111111000000000000000022-1-1-1-10000
χ3522222-1-1-1-12222-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-2-2-2-2222211-1-1111111111100001i3−i3i3i3−i3−i31i3−i3-1-1-1-1000000000000000000−i3i3−i3i30000
χ3622222-1-1-1-12222-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-2-2-2-2222211-1-1111111111100001−i3i3−i3−i3i3i31−i3i3-1-1-1-1000000000000000000i3−i3i3−i30000
χ3722222-1-1-1-1-2-2-2-222-2-2222222-11111-1-1-1-1-1-22-2-222-2-2-1-111-1-1-1-11111-1-122-2-21-1-111111-1-1-1-11100000000000000002-2-1-1110000
χ3822222-1-1-1-1-2-2-2-222-2-2222222-11111-1-1-1-1-1-22-2-222-2-2-1-111-1-1-1-11111-1-1-2-222111-1-1-1-1111-1-1110000000000000000-2211-1-10000
χ3922222-1-1-1-1-2-2-2-222-2-222-2-2-2-2-11111-1-1-1-1-122-22-2-2221111-1-1-1-11111110000-1i3−i3−i3−i3i3i3-1i3−i311-1-1000000000000000000i3−i3−i3i30000
χ4022222-1-1-1-1-2-2-2-222-2-222-2-2-2-2-11111-1-1-1-1-122-22-2-2221111-1-1-1-11111110000-1−i3i3i3i3−i3−i3-1−i3i311-1-1000000000000000000−i3i3i3−i30000
χ4122222-1-1-1-1-2-2-2-2-2-222222222-11111-1-1-1-1-1-2-22-2-2-222-1-1111111-1-1-1-1-1-122-2-21-1-111111-1-111-1-10000000000000000-2211-1-10000
χ4222222-1-1-1-1-2-2-2-2-2-222222222-11111-1-1-1-1-1-2-22-2-2-222-1-1111111-1-1-1-1-1-1-2-222111-1-1-1-111111-1-100000000000000002-2-1-1110000
χ4322222-1-1-1-1-2-2-2-2-2-22222-2-2-2-2-11111-1-1-1-1-12-22222-2-211111111-1-1-1-1110000-1i3−i3−i3−i3i3i3-1i3−i3-1-111000000000000000000−i3i3i3−i30000
χ4422222-1-1-1-1-2-2-2-2-2-22222-2-2-2-2-11111-1-1-1-1-12-22222-2-211111111-1-1-1-1110000-1−i3i3i3i3−i3−i3-1−i3i3-1-111000000000000000000i3−i3−i3i30000
χ4522-2-222-2-22000000222-22-22-2-2000022-2-2200-20002-22-200000022-2-22-200000000000000002-202200-2-20002-22-2000000000000
χ4622-2-222-2-22000000222-22-22-2-2000022-2-2200-20002-22-200000022-2-22-200000000000000002-20-2-20022000-22-22000000000000
χ4722-2-222-2-22000000222-2-22-22-2000022-2-2200-2000-22-2200000022-2-2-220000000000000000-222002-200-22-200002-20000000000
χ4822-2-222-2-22000000222-2-22-22-2000022-2-2200-2000-22-2200000022-2-2-220000000000000000-22-200-22002-220000-220000000000
χ4922-2-222-2-22000000-2-22-22-22-2-2000022-2-22002000-222-2000000-2-2222-20000000000000000-2202-200-220002-2-22000000000000
χ5022-2-222-2-22000000-2-22-22-22-2-2000022-2-22002000-222-2000000-2-2222-20000000000000000-220-22002-2000-222-2000000000000
χ5122-2-222-2-22000000-2-22-2-22-22-2000022-2-220020002-2-22000000-2-222-2200000000000000002-2200-2-20022-20000-220000000000
χ5222-2-222-2-22000000-2-22-2-22-22-2000022-2-220020002-2-22000000-2-222-2200000000000000002-2-2002200-2-2200002-20000000000
χ5322-2-222-2-2200002200-222-2-22-20000-2-22220-2002-2002-20022-2-20000-22000000000000002-20002020-20-200-2200-220000000000
χ5422-2-222-2-2200002200-222-2-22-20000-2-22220-2002-2002-20022-2-20000-22000000000000002-2000-20-20202002-2002-20000000000
χ5522-2-222-2-2200002200-22-222-2-20000-2-22220-200-2200-220022-2-200002-200000000000000-22002020-20-20-2200-22000000000000
χ5622-2-222-2-2200002200-22-222-2-20000-2-22220-200-2200-220022-2-200002-200000000000000-2200-20-2020202-2002-2000000000000
χ5722-2-222-2-220000-2-200-222-2-22-20000-2-22220200-22002-200-2-2220000-2200000000000000-2200020-20-20200-22002-20000000000
χ5822-2-222-2-220000-2-200-222-2-22-20000-2-22220200-22002-200-2-2220000-2200000000000000-22000-202020-2002-200-220000000000
χ5922-2-222-2-220000-2-200-22-222-2-20000-2-222202002-200-2200-2-22200002-2000000000000002-20020-20-2020-22002-2000000000000
χ6022-2-222-2-220000-2-200-22-222-2-20000-2-222202002-200-2200-2-22200002-2000000000000002-200-202020-202-200-22000000000000
χ6144444-2-2-2-244-4-40000-4-444-4-4-2-2-2-2-22222-2400-40000-2-22200000000220000-2000000200000000000000000000000000000000
χ6244444-2-2-2-244-4-40000-4-4-4-444-2-2-2-2-22222-2-40040000222200000000-2-200002000000-200000000000000000000000000000000
χ6344444-2-2-2-2-4-4440000-4-444-4-4-222222222-2-40040000-2-2-2-2000000002200002000000-200000000000000000000000000000000
χ6444444-2-2-2-2-4-4440000-4-4-4-444-222222222-2400-4000022-2-200000000-2-20000-2000000200000000000000000000000000000000
χ6544-44-44444004-40000000000-400000000-400000000004-400000000002-22-20222-22-20-2-2000000000000000000000000000000
χ6644-44-44444004-40000000000-400000000-400000000004-40000000000-22-220-2-2-22-22022000000000000000000000000000000
χ6744-44-4444400-440000000000-400000000-40000000000-4400000000002-2-22022-22-220-2-2000000000000000000000000000000
χ6844-44-4444400-440000000000-400000000-40000000000-440000000000-222-20-2-22-22-2022000000000000000000000000000000
χ6944-44-4-2-2-2-2004-4000000000022i32i3−2i3−2i32i3−2i32i3−2i320000000000-2200000000002-22-20−1+i3−1−i3−1+i31−i3−1−i31+i301−i31+i3000000000000000000000000000000
χ7044-44-4-2-2-2-2004-4000000000022i32i3−2i3−2i32i3−2i32i3−2i320000000000-220000000000-22-2201−i31+i31−i3−1+i31+i3−1−i30−1+i3−1−i3000000000000000000000000000000
χ7144-44-4-2-2-2-2004-400000000002−2i3−2i32i32i3−2i32i3−2i32i320000000000-2200000000002-22-20−1−i3−1+i3−1−i31+i3−1+i31−i301+i31−i3000000000000000000000000000000
χ7244-44-4-2-2-2-2004-400000000002−2i3−2i32i32i3−2i32i3−2i32i320000000000-220000000000-22-2201+i31−i31+i3−1−i31−i3−1+i30−1−i3−1+i3000000000000000000000000000000
χ7344-44-4-2-2-2-200-44000000000022i32i3−2i3−2i3−2i32i3−2i32i3200000000002-200000000002-2-220−1−i3−1+i31+i3−1−i31−i3−1+i301+i31−i3000000000000000000000000000000
χ7444-44-4-2-2-2-200-44000000000022i32i3−2i3−2i3−2i32i3−2i32i3200000000002-20000000000-222-201+i31−i3−1−i31+i3−1+i31−i30−1−i3−1+i3000000000000000000000000000000
χ7544-44-4-2-2-2-200-4400000000002−2i3−2i32i32i32i3−2i32i3−2i3200000000002-200000000002-2-220−1+i3−1−i31−i3−1+i31+i3−1−i301−i31+i3000000000000000000000000000000
χ7644-44-4-2-2-2-200-4400000000002−2i3−2i32i32i32i3−2i32i3−2i3200000000002-20000000000-222-201−i31+i3−1+i31−i3−1−i31+i30−1+i3−1−i3000000000000000000000000000000
χ7744-4-44-222-2000000444-44-44-420000-2-222-200-40004-4-22000000-2-222-220000000000000000-2200000000000000000000000000
χ7844-4-44-222-2000000444-4-44-4420000-2-222-200-4000-442-2000000-2-2222-200000000000000002-200000000000000000000000000
χ7944-4-44-222-2000000-4-44-44-44-420000-2-222-2004000-44-2200000022-2-2-2200000000000000002-200000000000000000000000000
χ8044-4-44-222-2000000-4-44-4-44-4420000-2-222-20040004-42-200000022-2-22-20000000000000000-2200000000000000000000000000
χ8144-4-44-222-200004400-444-4-442000022-2-2-20-4004-400-2200-2-22200002-200000000000000-220000000000000000000000000000
χ8244-4-44-222-200004400-44-444-42000022-2-2-20-400-44002-200-2-2220000-22000000000000002-20000000000000000000000000000
χ8344-4-44-222-20000-4-400-444-4-442000022-2-2-20400-4400-220022-2-200002-2000000000000002-20000000000000000000000000000
χ8444-4-44-222-20000-4-400-44-444-42000022-2-2-204004-4002-20022-2-20000-2200000000000000-220000000000000000000000000000
χ85888-8-88-8-8800000000000000800000000-8000000000000000000000000000000000000000000000000000000000000000000
χ86888-8-8-444-400000000000000-400004i3−4i3−4i34i34000000000000000000000000000000000000000000000000000000000000000000
χ87888-8-8-444-400000000000000-40000−4i34i34i3−4i34000000000000000000000000000000000000000000000000000000000000000000
χ888-8000800-84-4004-44-400000004-44-4000000000000000004-4004-4000000000000000000000000000000000000000000000000
χ898-8000800-84-400-44-4400000004-44-400000000000000000-4400-44000000000000000000000000000000000000000000000000
χ908-8000800-8-44004-4-440000000-44-44000000000000000004-400-44000000000000000000000000000000000000000000000000
χ918-8000800-8-4400-444-40000000-44-4400000000000000000-44004-4000000000000000000000000000000000000000000000000
χ928-8000-44i3−4i344-4004-44-40000000−2+2i32−2i3−2−2i32+2i300000000000000000-222i3−2i3-222i3−2i30000000000000000000000000000000000000000000000
χ938-8000-44i3−4i344-400-44-440000000−2+2i32−2i3−2−2i32+2i3000000000000000002-2−2i32i32-2−2i32i30000000000000000000000000000000000000000000000
χ948-8000-44i3−4i34-44004-4-4400000002−2i3−2+2i32+2i3−2−2i300000000000000000-222i3−2i32-2−2i32i30000000000000000000000000000000000000000000000
χ958-8000-44i3−4i34-4400-444-400000002−2i3−2+2i32+2i3−2−2i3000000000000000002-2−2i32i3-222i3−2i30000000000000000000000000000000000000000000000
χ968-8000-4−4i34i344-4004-44-40000000−2−2i32+2i3−2+2i32−2i300000000000000000-22−2i32i3-22−2i32i30000000000000000000000000000000000000000000000
χ978-8000-4−4i34i344-400-44-440000000−2−2i32+2i3−2+2i32−2i3000000000000000002-22i3−2i32-22i3−2i30000000000000000000000000000000000000000000000
χ988-8000-4−4i34i34-44004-4-4400000002+2i3−2−2i32−2i3−2+2i300000000000000000-22−2i32i32-22i3−2i30000000000000000000000000000000000000000000000
χ998-8000-4−4i34i34-4400-444-400000002+2i3−2−2i32−2i3−2+2i3000000000000000002-22i3−2i3-22−2i32i30000000000000000000000000000000000000000000000

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