Finite Group Databasebeta

← Group #13181095

Character table — Group #13181095

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1122222444444444448888888888888812121212121212121212121212121212121216161618181818242424242424242424363636363636363636365454727272108108108
order1222346333366666612366666666612121212244466121212121212121212121212661224446661212121212122444612121212128861212888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-11111111111-1-1111-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1111
χ5111-11-1111111-11111-11111-1-1-11-11-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-11-11111111-1-1-111-1-1-111-1-1-11111-11-1-1
χ6111-11-1111111-11111-11111-1-1-11-11-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-11-11111111-1-1-1-1-111-111-111-1-1-1-11-111
χ7111-11-1111111-11111-11111-1-1-11-11-1-1-1-1-1-111-1-1-1-111111111111-1-1-11-11-1-1-1-1-1-111111-1-1-111-1-1-1-1-111-1-111
χ8111-11-1111111-11111-11111-1-1-11-11-1-1-1-1-1-111-1-1-1-111111111111-1-1-11-11-1-1-1-1-1-1111-1-111-111-11111-1-111-1-1
χ911-111-111111-111111-11-1-1-1111-111-1-1-1-11-11-111-1-111-1-1-1-1-1-1-1-1-11-1-1-111111-1-1-11111-11-1-11-11-1-1111-11-11-1
χ1011-111-111111-111111-11-1-1-1111-111-1-1-1-11-11-111-1-111-1-1-1-1-1-1-1-1-11-1-1-111111-1-1-1111-11-11-11-1111-1-1-11-11-11
χ1111-111-111111-111111-11-1-1-1111-111-1-1-1-1-11-11-1-111-1-111111111-11-1-1-111-1-1-1111-1-1-11-11-1-11-11-1-1-1-11-111-11
χ1211-111-111111-111111-11-1-1-1111-111-1-1-1-1-11-11-1-111-1-111111111-11-1-1-111-1-1-1111-1-1-1-11-11-11-111111-11-1-11-1
χ1311-1-11111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-11-1-1111-1-111111-1-1-1-11
χ1411-1-11111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-111-111-1-1-1-1-1-1-11111-1
χ1511-1-11111111-1-1111111-1-1-1-1-1-1-1-111111-111-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11-1-1-11111111-1-1111-1-111-1-11-1-111-1
χ1611-1-11111111-1-1111111-1-1-1-1-1-1-1-111111-111-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1111111-111-111-1-1-1-111-111-1-11
χ1722222222222222222222222222222222000000000000000000222-2-2-2-20000000000000-2-2-2-20000000000
χ182222-12-12-1-12-1-12-1-12-1-12-1-12-1-122-12-1-120000−i3i3−i3i3−i3i3−i3i300−i3−i3i3i3-1-1-1-2-2-2-20−i3i30−i3i30−i3i3000011110000000000
χ192222-12-12-1-12-1-12-1-12-1-12-1-12-1-122-12-1-120000i3−i3i3−i3i3−i3i3−i300i3i3−i3−i3-1-1-1-2-2-2-20i3−i30i3−i30i3−i3000011110000000000
χ202222-12-12-1-12-1-12-1-12-1-12-1-12-1-122-12-1-122222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-122222-1-12-1-12-1-10000-1-1-1-10000000000
χ212222-12-12-1-12-1-12-1-12-1-12-1-12-1-122-12-1-12-2-2-2-211111111-2-21111-1-1-12222-211-211-2110000-1-1-1-10000000000
χ22222-22-2222222-22222-22222-2-2-22-22-2-2-2-20000000000000000002-2-22-22-200000000000002-2-220000000000
χ23222-2-1-2-12-1-12-112-1-121-12-1-1-2112-2-1-211-20000−i3i3−i3i3i3−i3i3−i300i3i3−i3−i3-1112-22-20−i3i30−i3i30i3−i30000-111-10000000000
χ24222-2-1-2-12-1-12-112-1-121-12-1-1-2112-2-1-211-20000i3−i3i3−i3−i3i3−i3i300−i3−i3i3i3-1112-22-20i3−i30i3−i30−i3i30000-111-10000000000
χ25222-2-1-2-12-1-12-112-1-121-12-1-1-2112-2-1-211-222-2-2-1-1-1-11111-2-21111-111-22-222-1-12-1-1-21100001-1-110000000000
χ26222-2-1-2-12-1-12-112-1-121-12-1-1-2112-2-1-211-2-2-2221111-1-1-1-122-1-1-1-1-111-22-22-211-2112-1-100001-1-110000000000
χ2722-222-222222-222222-22-2-2-2222-222-2-2-2-2000000000000000000-22-222-2-200000000000002-22-20000000000
χ2822-22-1-2-12-1-121-12-1-121-1-2112-1-1-22-1-211-20000−i3i3i3−i3−i3i3i3−i300i3i3−i3−i31-1122-2-20−i3i30i3−i30−i3i30000-11-110000000000
χ2922-22-1-2-12-1-121-12-1-121-1-2112-1-1-22-1-211-20000i3−i3−i3i3i3−i3−i3i300−i3−i3i3i31-1122-2-20i3−i30−i3i30i3−i30000-11-110000000000
χ3022-22-1-2-12-1-121-12-1-121-1-2112-1-1-22-1-211-22-22-2-1-111-1-111-2-211111-11-2-2222-1-1-2112-1-100001-11-10000000000
χ3122-22-1-2-12-1-121-12-1-121-1-2112-1-1-22-1-211-2-22-2211-1-111-1-122-1-1-1-11-11-2-222-2112-1-1-21100001-11-10000000000
χ3222-2-22222222-2-2222222-2-2-2-2-2-2-2-222222000000000000000000-2-22-222-20000000000000-2-2220000000000
χ3322-2-2-12-12-1-12112-1-12-1-1-211-211-2-2-12-1-120000−i3i3i3−i3i3−i3−i3i300−i3−i3i3i311-1-222-20−i3i30i3−i30i3−i3000011-1-10000000000
χ3422-2-2-12-12-1-12112-1-12-1-1-211-211-2-2-12-1-120000i3−i3−i3i3−i3i3i3−i300i3i3−i3−i311-1-222-20i3−i30−i3i30−i3i3000011-1-10000000000
χ3522-2-2-12-12-1-12112-1-12-1-1-211-211-2-2-12-1-122-2-22-1-11111-1-122-1-1-1-111-12-2-222-1-1-211-2110000-1-1110000000000
χ3622-2-2-12-12-1-12112-1-12-1-1-211-211-2-2-12-1-12-222-211-1-1-1-111-2-2111111-12-2-22-2112-1-12-1-10000-1-1110000000000
χ374444444111-244111-24-2111111-2-2-2111-2222222222222-1-1-1-1-1-1-2-2-20000-1-1-1-1-1-1-1-1-1000000000000000000
χ384444444111-244111-24-2111111-2-2-2111-2-2-2-2-2-2-2-2-2-2-2-2-2111111-2-2-20000111111111000000000000000000
χ394444444-2-2-2144-2-2-2141-2-2-2-2-2-2111-2-2-21000000000000000000111000000000000022220000-1-100-1-1-1000
χ404444444-2-2-2144-2-2-2141-2-2-2-2-2-2111-2-2-210000000000000000001110000000000000-2-2-2-200001100111000
χ414444-24-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-2-211−1−3i32−1+3i321−1−3i32−1+3i32-2-211−1−3i32−1+3i32-22222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i321110000-11+i321−i32-11+i321−i32-11+i321−i32000000000000000000
χ424444-24-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-2-211−1−3i32−1+3i321−1−3i32−1+3i32-2-211−1−3i32−1+3i32-2-2-2-2-21+i31−i31+i31−i31+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211100001−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32000000000000000000
χ434444-24-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-2-211−1+3i32−1−3i321−1+3i32−1−3i32-2-211−1+3i32−1−3i32-22222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i321110000-11−i321+i32-11−i321+i32-11−i321+i32000000000000000000
χ444444-24-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-2-211−1+3i32−1−3i321−1+3i32−1−3i32-2-211−1+3i32−1−3i32-2-2-2-2-21−i31+i31−i31+i31−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211100001−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32000000000000000000
χ45444-44-44111-24-4111-2-4-2111-1-1-1-22-2-1-1-1222-2-22222-2-2-2-2111111-2220000-1-1-1-1-1-1111000000000000000000
χ46444-44-44111-24-4111-2-4-2111-1-1-1-22-2-1-1-12-2-222-2-2-2-22222-1-1-1-1-1-1-2220000111111-1-1-1000000000000000000
χ47444-44-44-2-2-214-4-2-2-21-41-2-2-22221-11222-10000000000000000001-1-1000000000000022-2-200001100-1-11000
χ48444-44-44-2-2-214-4-2-2-21-41-2-2-22221-11222-10000000000000000001-1-10000000000000-2-2220000-1-10011-1000
χ49444-4-2-4-21−1−3i32−1+3i32-2-221−1−3i32−1+3i32-2211−1−3i32−1+3i32-11+3i321−3i32-221-11+3i321−3i32222-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i321-1-10000-11+i321−i32-11+i321−i321−1−i32−1+i32000000000000000000
χ50444-4-2-4-21−1−3i32−1+3i32-2-221−1−3i32−1+3i32-2211−1−3i32−1+3i32-11+3i321−3i32-221-11+3i321−3i322-2-2221+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i321-1-100001−1−i32−1+i321−1−i32−1+i32-11+i321−i32000000000000000000
χ51444-4-2-4-21−1+3i32−1−3i32-2-221−1+3i32−1−3i32-2211−1+3i32−1−3i32-11−3i321+3i32-221-11−3i321+3i32222-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i321-1-10000-11−i321+i32-11−i321+i321−1+i32−1−i32000000000000000000
χ52444-4-2-4-21−1+3i32−1−3i32-2-221−1+3i32−1−3i32-2211−1+3i32−1−3i32-11−3i321+3i32-221-11−3i321+3i322-2-2221−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i321-1-100001−1+i32−1−i321−1+i32−1−i32-11−i321+i32000000000000000000
χ5344-444-44111-2-44111-2-4-2-1-1-11112-2-2-1-1-122-22-222-2-222-2-21111112-220000-1-1-1111-1-1-1000000000000000000
χ5444-444-44111-2-44111-2-4-2-1-1-11112-2-2-1-1-12-22-22-2-222-2-222-1-1-1-1-1-12-220000111-1-1-1111000000000000000000
χ5544-444-44-2-2-21-44-2-2-21-41222-2-2-2-111222-1000000000000000000-11-100000000000002-22-200001100-11-1000
χ5644-444-44-2-2-21-44-2-2-21-41222-2-2-2-111222-1000000000000000000-11-10000000000000-22-220000-1-1001-11000
χ5744-44-2-4-21−1−3i32−1+3i32-22-21−1−3i32−1+3i32-221-11+3i321−3i321−1−3i32−1+3i322-21-11+3i321−3i3222-22-2−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i311−1−i32−1−i32−1+i32−1+i32-11-10000-11+i321−i321−1−i32−1+i32-11+i321−i32000000000000000000
χ5844-44-2-4-21−1−3i32−1+3i32-22-21−1−3i32−1+3i32-221-11+3i321−3i321−1−3i32−1+3i322-21-11+3i321−3i322-22-221+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i3-1-11+i321+i321−i321−i32-11-100001−1−i32−1+i32-11+i321−i321−1−i32−1+i32000000000000000000
χ5944-44-2-4-21−1+3i32−1−3i32-22-21−1+3i32−1−3i32-221-11−3i321+3i321−1+3i32−1−3i322-21-11−3i321+3i3222-22-2−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i311−1+i32−1+i32−1−i32−1−i32-11-10000-11−i321+i321−1+i32−1−i32-11−i321+i32000000000000000000
χ6044-44-2-4-21−1+3i32−1−3i32-22-21−1+3i32−1−3i32-221-11−3i321+3i321−1+3i32−1−3i322-21-11−3i321+3i322-22-221−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i3-1-11−i321−i321+i321+i32-11-100001−1+i32−1−i32-11−i321+i321−1+i32−1−i32000000000000000000
χ6144-4-4444111-2-4-4111-24-2-1-1-1-1-1-122-2111-22-2-2222-2-2-2-222-1-1-1-1-1-122-20000-1-1-1111111000000000000000000
χ6244-4-4444111-2-4-4111-24-2-1-1-1-1-1-122-2111-2-222-2-2-22222-2-211111122-20000111-1-1-1-1-1-1000000000000000000
χ6344-4-4444-2-2-21-4-4-2-2-2141222222-1-11-2-2-21000000000000000000-1-1100000000000002-2-220000-1-100-111000
χ6444-4-4444-2-2-21-4-4-2-2-2141222222-1-11-2-2-21000000000000000000-1-110000000000000-222-2000011001-1-1000
χ6544-4-4-24-21−1−3i32−1+3i32-2221−1−3i32−1+3i32-2-21-11+3i321−3i32-11+3i321−3i322211−1−3i32−1+3i32-22-2-22−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-110000-11+i321−i321−1−i32−1+i321−1−i32−1+i32000000000000000000
χ6644-4-4-24-21−1−3i32−1+3i32-2221−1−3i32−1+3i32-2-21-11+3i321−3i32-11+3i321−3i322211−1−3i32−1+3i32-2-222-21+i31−i3−1−i3−1+i3−1−i3−1+i31+i31−i311−1−i32−1−i32−1+i32−1+i32-1-1100001−1−i32−1+i32-11+i321−i32-11+i321−i32000000000000000000
χ6744-4-4-24-21−1+3i32−1−3i32-2221−1+3i32−1−3i32-2-21-11−3i321+3i32-11−3i321+3i322211−1+3i32−1−3i32-22-2-22−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-110000-11−i321+i321−1+i32−1−i321−1+i32−1−i32000000000000000000
χ6844-4-4-24-21−1+3i32−1−3i32-2221−1+3i32−1−3i32-2-21-11−3i321+3i32-11−3i321+3i322211−1+3i32−1−3i32-2-222-21−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i311−1+i32−1+i32−1−i32−1−i32-1-1100001−1+i32−1−i32-11−i321+i32-11−i321+i32000000000000000000
χ694-40040-4444400-4-4-4-40400000000-400000000000000000000000000000000000000000000000022−22000000
χ704-40040-4444400-4-4-4-40400000000-4000000000000000000000000000000000000000000000000−2222000000
χ718888-48-4-4222-4-4-4222-4-1-422-42222-1-4222000000000000000000-1-1-10000000000000000000000000000000
χ72888-8-4-8-4-4222-44-42224-1-4224-2-22-2-14-2-2-2000000000000000000-1110000000000000000000000000000000
χ7388-88-4-8-4-42224-4-42224-14-2-2-422-22-14-2-2-20000000000000000001-110000000000000000000000000000000
χ7488-8-8-48-4-422244-4222-4-14-2-24-2-2-2-2-1-422200000000000000000011-10000000000000000000000000000000
χ758-80080-8222-400-2-2-240-4000000004000000000000000023−2323−2323−230000000000000000000000000000000000
χ768-80080-8222-400-2-2-240-40000000040000000000000000−2323−2323−23230000000000000000000000000000000000
χ778-80080-8-4-4-4200444-20200000000-2000000000000000000000000000000000000000000000023−2300000000
χ788-80080-8-4-4-4200444-20200000000-20000000000000000000000000000000000000000000000−232300000000
χ798-800-4042−1−3i3−1+3i3-400-21+3i31−3i340200000000-2000000000000000023−234ζ14+2ζ22−4ζ14−2ζ22−2ζ14−4ζ222ζ14+4ζ220000000000000000000000000000000000
χ808-800-4042−1−3i3−1+3i3-400-21+3i31−3i340200000000-20000000000000000−2323−4ζ14−2ζ224ζ14+2ζ222ζ14+4ζ22−2ζ14−4ζ220000000000000000000000000000000000
χ818-800-4042−1+3i3−1−3i3-400-21−3i31+3i340200000000-2000000000000000023−23−2ζ14−4ζ222ζ14+4ζ224ζ14+2ζ22−4ζ14−2ζ220000000000000000000000000000000000
χ828-800-4042−1+3i3−1−3i3-400-21−3i31+3i340200000000-20000000000000000−23232ζ14+4ζ22−2ζ14−4ζ22−4ζ14−2ζ224ζ14+2ζ220000000000000000000000000000000000
χ838-800-4048-4-4800-844-80-400000000400000000000000000000000000000000000000000000000000000000
χ8416-1600-808-8444008-4-4-40-200000000200000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.