Finite Group Databasebeta

← Group #13181098

Character table — Group #13181098

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11222224444444444466666688888888888888991212121212121212121212121212121616161818181818181824242424242424242436363636363636365454727272108108108
order1222346333366666612226666366666666612121212222246666666666121266122244466666666121212244661212124461212444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-111111111111-1-1-1111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111111111-1-1111-1-1-1
χ4111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1111
χ5111-11-1111111-11111-111111111111-1-1-1-11-1-1-1-1111-1-111-1-1111111-1-11-1-11-1-11111111-1-1-1-1-1-1-11-11-1-11111-11-1-11-1
χ6111-11-1111111-11111-111111111111-1-1-1-11-1-1-1-1111-1-111-1-1111111-1-11-1-11-1-1-1-111111-1-1-1-1-1-11-111-1-1-1-1-1-11-111-11
χ7111-11-1111111-11111-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-111-111-1-111-1-1-1-1-1-1111-1-11-1-11111-1-1-1111111-11-11-1-111-1-1-11-11-11
χ8111-11-1111111-11111-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-111-111-1-111-1-1-1-1-1-1111-1-11-1-1-1-111-1-1-11111111-111-1-1-1-1111-11-11-1
χ911-111-111111-111111-11111111-1-1-1-111111-1-1-1-111-11-1-1-111111111-1-1-11-1-11-11111-1-1-1111-1-1-1-1-11-11-11111-1-11-1-11
χ1011-111-111111-111111-11111111-1-1-1-111111-1-1-1-111-11-1-1-111111111-1-1-11-1-11-1-1-111-1-1-1111-1-1-111-1-11-1-1-1-1-111-111-1
χ1111-111-111111-111111-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1111-1111-1-1-1-1-1-1-1-111-11-1-11-11111111-1-1-1111-1-11-11-111-1-1-1-1111-1
χ1211-111-111111-111111-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1111-1111-1-1-1-1-1-1-1-111-11-1-11-1-1-111111-1-1-111111-1-11-1-1-11111-1-1-11
χ1311-1-11111111-1-1111111111111-1-1-1-1-1-1-1-11111111-1-11-1-1-1-111111111-1-11-1-111111-1-1-1-1-1-11111-1-1-1-1111111-1-11-1-1
χ1411-1-11111111-1-1111111111111-1-1-1-1-1-1-1-11111111-1-11-1-1-1-111111111-1-11-1-11-1-111-1-1-1-1-1-1111-111-1-11-1-1-1-1-111-111
χ1511-1-11111111-1-111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-11111-1-1-1-1-1-1-1-1-1-11-1-111111111111-1-1-11-1-1-1-1111-1-11-1-1-111
χ1611-1-11111111-1-111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-11111-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111-1-1-1-111-1-11-1-111-1111-1-1
χ1722222222222222222200000022222222222222-2-2000000000000000222-2-2-200-2-2000000000000-2-2-20000000000
χ182222-12-122-1-1-1-12-1-12-100−i3−i3i3i3-122-1-122-1-1-12-1-12-2-2000−i3i3−i3i300−i3−i3i3i3−i3i3-1-1-1-2-2-200110−i3i30−i3i30−i3i30001110000000000
χ192222-12-122-1-1-1-12-1-12-100i3i3−i3−i3-122-1-122-1-1-12-1-12-2-2000i3−i3i3−i300i3i3−i3−i3i3−i3-1-1-1-2-2-200110i3−i30i3−i30i3−i30001110000000000
χ202222-12-122-1-1-1-12-1-12-122-1-1-1-1-122-1-122-1-1-12-1-1222222-1-1-1-122-1-1-1-1-1-1-1-1-122200-1-12-1-12-1-12-1-1000-1-1-10000000000
χ212222-12-122-1-1-1-12-1-12-1-2-21111-122-1-122-1-1-12-1-1222-2-2-21111-2-2111111-1-1-122200-1-1-211-211-211000-1-1-10000000000
χ22222-22-2222222-22222-200000022222-2-2-2-22-2-2-2-2-2-20000000000000002-2-2-22200-2-2000000000000-2220000000000
χ23222-2-1-2-122-1-1-112-1-12100−i3−i3i3i3-122-1-1-2-211-1-211-2-2-2000−i3i3i3−i300−i3−i3i3i3i3−i3-111-22200110−i3i30i3−i30i3−i30001-1-10000000000
χ24222-2-1-2-122-1-1-112-1-12100i3i3−i3−i3-122-1-1-2-211-1-211-2-2-2000i3−i3−i3i300i3i3−i3−i3−i3i3-111-22200110i3−i30−i3i30−i3i30001-1-10000000000
χ25222-2-1-2-122-1-1-112-1-12122-1-1-1-1-122-1-1-2-211-1-211-2222-2-2-1-11122-1-1-1-111-1112-2-200-1-12-1-1-211-211000-1110000000000
χ26222-2-1-2-122-1-1-112-1-121-2-21111-122-1-1-2-211-1-211-222-22211-1-1-2-21111-1-1-1112-2-200-1-1-2112-1-12-1-1000-1110000000000
χ2722-222-222222-222222-20000002-2-2-2-222222-2-2-2-2-2-2000000000000000-22-22-2200-2-20000000000002-220000000000
χ2822-22-1-2-122-1-11-12-1-12100−i3−i3i3i3-1-2-21122-1-1-1-211-2-2-2000i3−i3−i3i300−i3−i3i3i3i3−i31-112-2200110i3−i30−i3i30i3−i3000-11-10000000000
χ2922-22-1-2-122-1-11-12-1-12100i3i3−i3−i3-1-2-21122-1-1-1-211-2-2-2000−i3i3i3−i300i3i3−i3−i3−i3i31-112-2200110−i3i30i3−i30−i3i3000-11-10000000000
χ3022-22-1-2-122-1-11-12-1-12122-1-1-1-1-1-2-21122-1-1-1-211-222-22-211-1-122-1-1-1-1111-11-22-200-1-1-2112-1-1-2110001-110000000000
χ3122-22-1-2-122-1-11-12-1-121-2-21111-1-2-21122-1-1-1-211-2222-22-1-111-2-21111-1-11-11-22-200-1-12-1-1-2112-1-10001-110000000000
χ3222-2-22222222-2-2222220000002-2-2-2-2-2-2-2-222222-2-2000000000000000-2-2222-200-2-200000000000022-20000000000
χ3322-2-2-12-122-1-1112-1-12-100−i3−i3i3i3-1-2-211-2-211-12-1-12-2-2000i3−i3i3−i300−i3−i3i3i3−i3i311-122-200110i3−i30i3−i30−i3i3000-1-110000000000
χ3422-2-2-12-122-1-1112-1-12-100i3i3−i3−i3-1-2-211-2-211-12-1-12-2-2000−i3i3−i3i300i3i3−i3−i3i3−i311-122-200110−i3i30−i3i30i3−i3000-1-110000000000
χ3522-2-2-12-122-1-1112-1-12-122-1-1-1-1-1-2-211-2-211-12-1-1222-2-22111122-1-1-1-1-1-111-1-2-2200-1-1-211-2112-1-100011-10000000000
χ3622-2-2-12-122-1-1112-1-12-1-2-21111-1-2-211-2-211-12-1-122222-2-1-1-1-1-2-211111111-1-2-2200-1-12-1-12-1-1-21100011-10000000000
χ372-20020-2222200-2-2-2-202-22-22-2200000000-200002-200000002-22-22-2000000002i−2i2-20000000000000002i−2i2i−2i000000
χ382-20020-2222200-2-2-2-202-22-22-2200000000-200002-200000002-22-22-200000000−2i2i2-2000000000000000−2i2i−2i2i000000
χ392-20020-2222200-2-2-2-20-22-22-22200000000-200002-20000000-22-22-22000000002i−2i2-20000000000000002i−2i−2i2i000000
χ402-20020-2222200-2-2-2-20-22-22-22200000000-200002-20000000-22-22-2200000000−2i2i2-2000000000000000−2i2i2i−2i000000
χ4144444441-21144111-24222222-21-2111-211-2111-2002222222-1-1-1-1-1-122-2-2-20000000-1-1-1-1-1-1-1-1-10000000000000000
χ4244444441-21144111-24-2-2-2-2-2-2-21-2111-211-2111-200-2-2-2-2-2-2-2111111-2-2-2-2-200000001111111110000000000000000
χ434444444-21-2-244-2-2-2140000001-21-2-2-21-2-21-2-2-21000000000000000001110002200000000000222000-1-100-1-1-1000
χ444444444-21-2-244-2-2-2140000001-21-2-2-21-2-21-2-2-2100000000000000000111000-2-200000000000-2-2-20001100111000
χ454444-24-21-2−1−3i32−1+3i32-2-21−1−3i32−1+3i32-2-222−1−i3−1−i3−1+i3−1+i311-2−1−3i32−1+3i321-2−1−3i32−1+3i3211−1−3i32−1+3i32-200222−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32−1−i3−1+i31110000000-11+i321−i32-11+i321−i32-11+i321−i320000000000000000
χ464444-24-21-2−1−3i32−1+3i32-2-21−1−3i32−1+3i32-2-2-2-21+i31+i31−i31−i311-2−1−3i32−1+3i321-2−1−3i32−1+3i3211−1−3i32−1+3i32-200-2-2-21+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i321+i31−i311100000001−1−i32−1+i321−1−i32−1+i321−1−i32−1+i320000000000000000
χ474444-24-21-2−1+3i32−1−3i32-2-21−1+3i32−1−3i32-2-222−1+i3−1+i3−1−i3−1−i311-2−1+3i32−1−3i321-2−1+3i32−1−3i3211−1+3i32−1−3i32-200222−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32−1+i3−1−i31110000000-11−i321+i32-11−i321+i32-11−i321+i320000000000000000
χ484444-24-21-2−1+3i32−1−3i32-2-21−1+3i32−1−3i32-2-2-2-21−i31−i31+i31+i311-2−1+3i32−1−3i321-2−1+3i32−1−3i3211−1+3i32−1−3i32-200-2-2-21−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i321−i31+i311100000001−1+i32−1−i321−1+i32−1−i321−1+i32−1−i320000000000000000
χ49444-44-441-2114-4111-2-4222222-21-211-12-1-1-2-1-1-12002-2-222-2-2-1-1-1-1-1-1-2-2-2220000000-1-1-11111110000000000000000
χ50444-44-441-2114-4111-2-4-2-2-2-2-2-2-21-211-12-1-1-2-1-1-1200-222-2-22211111122-2220000000111-1-1-1-1-1-10000000000000000
χ51444-44-44-21-2-24-4-2-2-21-40000001-21-2-22-1221222-1000000000000000001-1-10002200000000000-22-2000-1-1001-11000
χ52444-44-44-21-2-24-4-2-2-21-40000001-21-2-22-1221222-1000000000000000001-1-1000-2-2000000000002-220001100-11-1000
χ53444-4-2-4-21-2−1−3i32−1+3i32-221−1−3i32−1+3i32-2222−1−i3−1−i3−1+i3−1+i311-2−1−3i32−1+3i32-121+3i321−3i321-11+3i321−3i322002-2-2−1−i3−1+i31+i31−i3-1-11+i321+i321−i321−i321+i31−i31-1-10000000-11+i321−i321−1−i32−1+i321−1−i32−1+i320000000000000000
χ54444-4-2-4-21-2−1−3i32−1+3i32-221−1−3i32−1+3i32-22-2-21+i31+i31−i31−i311-2−1−3i32−1+3i32-121+3i321−3i321-11+3i321−3i32200-2221+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32−1−i3−1+i31-1-100000001−1−i32−1+i32-11+i321−i32-11+i321−i320000000000000000
χ55444-4-2-4-21-2−1+3i32−1−3i32-221−1+3i32−1−3i32-2222−1+i3−1+i3−1−i3−1−i311-2−1+3i32−1−3i32-121−3i321+3i321-11−3i321+3i322002-2-2−1+i3−1−i31−i31+i3-1-11−i321−i321+i321+i321−i31+i31-1-10000000-11−i321+i321−1+i32−1−i321−1+i32−1−i320000000000000000
χ56444-4-2-4-21-2−1+3i32−1−3i32-221−1+3i32−1−3i32-22-2-21−i31−i31+i31+i311-2−1+3i32−1−3i32-121−3i321+3i321-11−3i321+3i32200-2221−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32−1+i3−1−i31-1-100000001−1+i32−1−i32-11−i321+i32-11−i321+i320000000000000000
χ5744-444-441-211-44111-2-4222222-2-12-1-11-211-2-1-1-1200-22-2-2-222-1-1-1-1-1-1-2-22-220000000111-1-1-11110000000000000000
χ5844-444-441-211-44111-2-4-2-2-2-2-2-2-2-12-1-11-211-2-1-1-12002-2222-2-2111111222-220000000-1-1-1111-1-1-10000000000000000
χ5944-444-44-21-2-2-44-2-2-21-400000012-122-21-2-21222-100000000000000000-11-10002200000000000-2-22000-1-10011-1000
χ6044-444-44-21-2-2-44-2-2-21-400000012-122-21-2-21222-100000000000000000-11-1000-2-20000000000022-20001100-1-11000
χ6144-44-2-4-21-2−1−3i32−1+3i322-21−1−3i32−1+3i32-2222−1−i3−1−i3−1+i3−1+i31-121+3i321−3i321-2−1−3i32−1+3i321-11+3i321−3i32200-22-21+i31−i3−1−i3−1+i3-1-11+i321+i321−i321−i321+i31−i3-11-100000001−1−i32−1+i32-11+i321−i321−1−i32−1+i320000000000000000
χ6244-44-2-4-21-2−1−3i32−1+3i322-21−1−3i32−1+3i32-22-2-21+i31+i31−i31−i31-121+3i321−3i321-2−1−3i32−1+3i321-11+3i321−3i322002-22−1−i3−1+i31+i31−i311−1−i32−1−i32−1+i32−1+i32−1−i3−1+i3-11-10000000-11+i321−i321−1−i32−1+i32-11+i321−i320000000000000000
χ6344-44-2-4-21-2−1+3i32−1−3i322-21−1+3i32−1−3i32-2222−1+i3−1+i3−1−i3−1−i31-121−3i321+3i321-2−1+3i32−1−3i321-11−3i321+3i32200-22-21−i31+i3−1+i3−1−i3-1-11−i321−i321+i321+i321−i31+i3-11-100000001−1+i32−1−i32-11−i321+i321−1+i32−1−i320000000000000000
χ6444-44-2-4-21-2−1+3i32−1−3i322-21−1+3i32−1−3i32-22-2-21−i31−i31+i31+i31-121−3i321+3i321-2−1+3i32−1−3i321-11−3i321+3i322002-22−1+i3−1−i31−i31+i311−1+i32−1+i32−1−i32−1−i32−1+i3−1−i3-11-10000000-11−i321+i321−1+i32−1−i32-11−i321+i320000000000000000
χ6544-4-44441-211-4-4111-24222222-2-12-1-1-12-1-1-2111-200-2-22-2-2-2-2-1-1-1-1-1-12222-20000000111111-1-1-10000000000000000
χ6644-4-44441-211-4-4111-24-2-2-2-2-2-2-2-12-1-1-12-1-1-2111-20022-22222111111-2-222-20000000-1-1-1-1-1-11110000000000000000
χ6744-4-4444-21-2-2-4-4-2-2-21400000012-1222-1221-2-2-2100000000000000000-1-1100022000000000002-2-2000-1-100-111000
χ6844-4-4444-21-2-2-4-4-2-2-21400000012-1222-1221-2-2-2100000000000000000-1-11000-2-200000000000-22200011001-1-1000
χ6944-4-4-24-21-2−1−3i32−1+3i32221−1−3i32−1+3i32-2-222−1−i3−1−i3−1+i3−1+i31-121+3i321−3i32-121+3i321−3i3211−1−3i32−1+3i32-200-2-221+i31−i31+i31−i3-1-11+i321+i321−i321−i32−1−i3−1+i3-1-1100000001−1−i32−1+i321−1−i32−1+i32-11+i321−i320000000000000000
χ7044-4-4-24-21-2−1−3i32−1+3i32221−1−3i32−1+3i32-2-2-2-21+i31+i31−i31−i31-121+3i321−3i32-121+3i321−3i3211−1−3i32−1+3i32-20022-2−1−i3−1+i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i321+i31−i3-1-110000000-11+i321−i32-11+i321−i321−1−i32−1+i320000000000000000
χ7144-4-4-24-21-2−1+3i32−1−3i32221−1+3i32−1−3i32-2-222−1+i3−1+i3−1−i3−1−i31-121−3i321+3i32-121−3i321+3i3211−1+3i32−1−3i32-200-2-221−i31+i31−i31+i3-1-11−i321−i321+i321+i32−1+i3−1−i3-1-1100000001−1+i32−1−i321−1+i32−1−i32-11−i321+i320000000000000000
χ7244-4-4-24-21-2−1+3i32−1−3i32221−1+3i32−1−3i32-2-2-2-21−i31−i31+i31+i31-121−3i321+3i32-121−3i321+3i3211−1+3i32−1−3i32-20022-2−1+i3−1−i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i321−i31+i3-1-110000000-11−i321+i32-11−i321+i321−1+i32−1−i320000000000000000
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χ848-80080-8-42-4-400444-20000000200000000-20000000000000000000000000004i−4i00000000000000000−2i2i00000000
χ858-80080-8-42-4-400444-20000000200000000-2000000000000000000000000000−4i4i000000000000000002i−2i00000000
χ868-800-4042-4−1−3i3−1+3i300-21+3i31−3i3404-4−2−2i32+2i3−2+2i32−2i3200000000-20000000000000-221+i3−1−i31−i3−1+i30000000000000000000000000000000000000
χ878-800-4042-4−1−3i3−1+3i300-21+3i31−3i340-442+2i3−2−2i32−2i3−2+2i3200000000-200000000000002-2−1−i31+i3−1+i31−i30000000000000000000000000000000000000
χ888-800-4042-4−1+3i3−1−3i300-21−3i31+3i3404-4−2+2i32−2i3−2−2i32+2i3200000000-20000000000000-221−i3−1+i31+i3−1−i30000000000000000000000000000000000000
χ898-800-4042-4−1+3i3−1−3i300-21−3i31+3i340-442−2i3−2+2i32+2i3−2−2i3200000000-200000000000002-2−1+i31−i3−1−i31+i30000000000000000000000000000000000000
χ9016-1600-808-8444008-4-4-40000000-200000000200000000000000000000000000000000000000000000000000000000

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