Finite Group Databasebeta

← Group #10690413

Character table — Group #10690413

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222222244444444448888888888888888888888888888881212121212121212121212121212121216161616242424244848
order12224444223444444666121212124466121212121212444444448888121212121212121212122424242424242424888888888888888812121212888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ51111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ61111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ91111-1-1-1-1-1-111111-1-1111-1-1-1-1-11-1-11111-1-111-1-1ii−i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1111-1-1-1-111-1-1i−ii−i1-1
χ101111-1-1-1-1-1-111111-1-1111-1-1-1-1-11-1-11111-1-111-1-1ii−i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-1-1-1111111-1-1−ii−ii-11
χ111111-1-1-1-1-1-111111-1-1111-1-1-1-1-11-1-11111-1-111-1-1−i−iii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-1-1-1111111-1-1i−ii−i-11
χ121111-1-1-1-1-1-111111-1-1111-1-1-1-1-11-1-11111-1-111-1-1−i−iii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1111-1-1-1-111-1-1−ii−ii1-1
χ131111-1-1-1-1-1-111111-1-1111-1-1-1-1-11-1-11111-1-1-1-111ii−i−i−i−iii1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-1-1-1-11111-1-111i−i−ii1-1
χ141111-1-1-1-1-1-111111-1-1111-1-1-1-1-11-1-11111-1-1-1-111ii−i−i−i−iii1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i1111-1-1-1-1-1-111−iii−i-11
χ151111-1-1-1-1-1-111111-1-1111-1-1-1-1-11-1-11111-1-1-1-111−i−iiiii−i−i1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii1111-1-1-1-1-1-111i−i−ii-11
χ161111-1-1-1-1-1-111111-1-1111-1-1-1-1-11-1-11111-1-1-1-111−i−iiiii−i−i1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-1-1-1-11111-1-111−iii−i1-1
χ1722222222222-2-222-2-22222222-2-22222-2-2-2-2000000000000-2-2000000000000000022220000000000000000-2-20000
χ1822222222222-2-222-2-22222222-2-22222-2-2-2-2000000000000-2-20000000000000000-2-2-2-20000000000000000220000
χ192222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-1000000
χ202222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-111111111111111110000000000000000-1-1-1-1000000
χ212222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000000000001111000000
χ222222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000000000001111000000
χ2322222222-2-2222-2-2222222222-2-2-2-2-2-22222000000000000-2-200000000000000000000222200000000000000-2-200
χ2422222222-2-2222-2-2222222222-2-2-2-2-2-22222000000000000-2-200000000000000000000-2-2-2-2000000000000002200
χ2522222222-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-22-22-20000000022000000000000000000000000000000002-22-2000000
χ2622222222-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-22-22000000002200000000000000000000000000000000-22-22000000
χ2722222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-122111111112-22-200000000-1-133−3−333−3−333−3−333−3−30000000000000000-11-11000000
χ2822222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-122111111112-22-200000000-1-1−3−333−3−333−3−333−3−3330000000000000000-11-11000000
χ2922222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-12211111111-22-2200000000-1-133−3−333−3−3−3−333−3−33300000000000000001-11-1000000
χ3022222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-12211111111-22-2200000000-1-1−3−333−3−33333−3−333−3−300000000000000001-11-1000000
χ312222-2-2-2-222222-2-2-2-2222-2-2-2-22-222-2-222-2-2000000000000-22000000000000000000002i2i−2i−2i00000000000000−2i2i00
χ322222-2-2-2-222222-2-2-2-2222-2-2-2-22-222-2-222-2-2000000000000-2200000000000000000000−2i−2i2i2i000000000000002i−2i00
χ332222-2-2-2-2222-2-2-2-222222-2-2-2-2-2222-2-2-2-2222-2-22000000002-2000000000000000000000000000000002-2-22000000
χ342222-2-2-2-2222-2-2-2-222222-2-2-2-2-2222-2-2-2-222-222-2000000002-200000000000000000000000000000000-222-2000000
χ352222-2-2-2-222-1-2-2-2-222-1-1-11111-22-1-11111-1-12-2-2200000000-11−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000-111-1000000
χ362222-2-2-2-222-1-2-2-2-222-1-1-11111-22-1-11111-1-12-2-2200000000-11i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000000000000000-111-1000000
χ372222-2-2-2-222-1-2-2-2-222-1-1-11111-22-1-11111-1-1-222-200000000-11−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000000000001-1-11000000
χ382222-2-2-2-222-1-2-2-2-222-1-1-11111-22-1-11111-1-1-222-200000000-11i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000001-1-11000000
χ392222-2-2-2-2-2-22-2-22222222-2-2-2-22-2-2-222-2-222000000000000-2200000000000000002i2i−2i−2i0000000000000000−2i2i0000
χ402222-2-2-2-2-2-22-2-22222222-2-2-2-22-2-2-222-2-222000000000000-220000000000000000−2i−2i2i2i00000000000000002i−2i0000
χ412222-2-2-2-2-2-2-12222-2-2-1-1-11111-2211-1-1-1-11122-2-22i2i−2i−2i2i2i−2i−2i-11−i−i−i−iiiii−i−i−i−iiiii0000000000000000-1-111000000
χ422222-2-2-2-2-2-2-12222-2-2-1-1-11111-2211-1-1-1-11122-2-2−2i−2i2i2i−2i−2i2i2i-11iiii−i−i−i−iiiii−i−i−i−i0000000000000000-1-111000000
χ432222-2-2-2-2-2-2-12222-2-2-1-1-11111-2211-1-1-1-111-2-2222i2i−2i−2i−2i−2i2i2i-11−i−i−i−iiiiiiiii−i−i−i−i000000000000000011-1-1000000
χ442222-2-2-2-2-2-2-12222-2-2-1-1-11111-2211-1-1-1-111-2-222−2i−2i2i2i2i2i−2i−2i-11iiii−i−i−i−i−i−i−i−iiiii000000000000000011-1-1000000
χ4522-2-22i−2i2i−2i0022-2002i−2i-22-22i2i−2i−2i0000002-22i−2i00001+i−1−i1−i−1+i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1322−2−2−i2−i2i2i20000000000
χ4622-2-22i−2i2i−2i0022-2002i−2i-22-22i2i−2i−2i0000002-22i−2i00001+i−1−i1−i−1+i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2−222i2i2−i2−i20000000000
χ4722-2-22i−2i2i−2i0022-2002i−2i-22-22i2i−2i−2i0000002-22i−2i0000−1−i1+i−1+i1−i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2−222i2i2−i2−i20000000000
χ4822-2-22i−2i2i−2i0022-2002i−2i-22-22i2i−2i−2i0000002-22i−2i0000−1−i1+i−1+i1−i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1322−2−2−i2−i2i2i20000000000
χ4922-2-2−2i2i−2i2i0022-200−2i2i-22-2−2i−2i2i2i0000002-2−2i2i00001−i−1+i1+i−1−i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2322−2−2i2i2−i2−i20000000000
χ5022-2-2−2i2i−2i2i0022-200−2i2i-22-2−2i−2i2i2i0000002-2−2i2i00001−i−1+i1+i−1−i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2−222−i2−i2i2i20000000000
χ5122-2-2−2i2i−2i2i0022-200−2i2i-22-2−2i−2i2i2i0000002-2−2i2i0000−1+i1−i−1−i1+i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2−222−i2−i2i2i20000000000
χ5222-2-2−2i2i−2i2i0022-200−2i2i-22-2−2i−2i2i2i0000002-2−2i2i0000−1+i1−i−1−i1+i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2322−2−2i2i2−i2−i20000000000
χ532-2-2222-2-2-222002-2002-2-22-22-200-222-2000000000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i22-22-20000−i2i2−i2i2−i2i2−i2i20000000000
χ542-2-2222-2-2-222002-2002-2-22-22-200-222-2000000000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2-22-220000i2−i2i2−i2i2−i2i2−i20000000000
χ552-2-2222-2-2-222002-2002-2-22-22-200-222-2000000000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i22-22-20000i2−i2i2−i2i2−i2i2−i20000000000
χ562-2-2222-2-2-222002-2002-2-22-22-200-222-2000000000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2-22-220000−i2i2−i2i2−i2i2−i2i20000000000
χ572-2-22-2-2222-22002-2002-2-2-22-22002-22-20000000000002−2−2200000000002−22−2−22−222i−2i−2i2i0000−i2i2−i2i2i2−i2i2−i20000000000
χ582-2-22-2-2222-22002-2002-2-2-22-22002-22-20000000000002−2−2200000000002−22−2−22−22−2i2i2i−2i0000i2−i2i2−i2−i2i2−i2i20000000000
χ592-2-22-2-2222-22002-2002-2-2-22-22002-22-2000000000000−222−20000000000−22−222−22−22i−2i−2i2i0000i2−i2i2−i2−i2i2−i2i20000000000
χ602-2-22-2-2222-22002-2002-2-2-22-22002-22-2000000000000−222−20000000000−22−222−22−2−2i2i2i−2i0000−i2i2−i2i2i2−i2i2−i20000000000
χ614444444444-2-4-444-4-4-2-2-2-2-2-2-2-4-4-2-2-2-2222200000000000022000000000000000000000000000000000000000000
χ6244444444-4-4-244-4-444-2-2-2-2-2-2-2-4-42222-2-2-2-200000000000022000000000000000000000000000000000000000000
χ634444-4-4-4-444-244-4-4-4-4-2-2-222224-4-2-222-2-2220000000000002-2000000000000000000000000000000000000000000
χ644444-4-4-4-4-4-4-2-4-44444-2-2-222224-422-2-222-2-20000000000002-2000000000000000000000000000000000000000000
χ6544-4-44i−4i4i−4i004-4400−4i4i-44-44i4i−4i−4i000000-44−4i4i00000000000000000000000000000000000000000000000000000000
χ6644-4-44i−4i4i−4i00-24-4004i−4i2-22−2i−2i2i2i000000-22−2i2i00002+2i−2−2i2−2i−2+2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000000000000000000000
χ6744-4-44i−4i4i−4i00-24-4004i−4i2-22−2i−2i2i2i000000-22−2i2i0000−2−2i2+2i−2+2i2−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000000000000000000000
χ6844-4-44i−4i4i−4i00-2-4400−4i4i2-22−2i−2i2i2i0000002-22i−2i00000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ220000000000000000000000000000000000
χ6944-4-44i−4i4i−4i00-2-4400−4i4i2-22−2i−2i2i2i0000002-22i−2i00000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ220000000000000000000000000000000000
χ7044-4-4−4i4i−4i4i004-44004i−4i-44-4−4i−4i4i4i000000-444i−4i00000000000000000000000000000000000000000000000000000000
χ7144-4-4−4i4i−4i4i00-24-400−4i4i2-222i2i−2i−2i000000-222i−2i00002−2i−2+2i2+2i−2−2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000000000000000000000
χ7244-4-4−4i4i−4i4i00-24-400−4i4i2-222i2i−2i−2i000000-222i−2i0000−2+2i2−2i−2−2i2+2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000000000000000000000
χ7344-4-4−4i4i−4i4i00-2-44004i−4i2-222i2i−2i−2i0000002-2−2i2i00000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ220000000000000000000000000000000000
χ7444-4-4−4i4i−4i4i00-2-44004i−4i2-222i2i−2i−2i0000002-2−2i2i00000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ220000000000000000000000000000000000
χ754-44-44i−4i−4i4i004000000-4-444i−4i−4i4i0000000000000000000000000000000000000000000000002i−2i−2i2i2-2-220000000000
χ764-44-44i−4i−4i4i004000000-4-444i−4i−4i4i000000000000000000000000000000000000000000000000−2i2i2i−2i-222-20000000000
χ774-44-4−4i4i4i−4i004000000-4-44−4i4i4i−4i0000000000000000000000000000000000000000000000002i−2i−2i2i-222-20000000000
χ784-44-4−4i4i4i−4i004000000-4-44−4i4i4i−4i000000000000000000000000000000000000000000000000−2i2i2i−2i2-2-220000000000
χ794-4-4444-4-44-4400-44004-4-44-44-4004-4-44000000000000000000000000000000000000000000000000000000000000
χ804-4-4444-4-44-4-200-4400-222-22-2200-222-200000000000000000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ814-4-4444-4-44-4-200-4400-222-22-2200-222-200000000000000000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ824-4-4444-4-4-44-2004-400-222-22-22002-2-22000000000000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ834-4-4444-4-4-44-2004-400-222-22-22002-2-220000000000002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ844-4-44-4-4444-4-2004-400-2222-22-200-22-2200000000000022−22−22220000000000−22−222−22−200000000000000000000000000
χ854-4-44-4-4444-4-2004-400-2222-22-200-22-22000000000000−222222−2200000000002−22−2−22−2200000000000000000000000000
χ864-4-44-4-444-44400-44004-4-4-44-4400-44-44000000000000000000000000000000000000000000000000000000000000
χ874-4-44-4-444-44-200-4400-2222-22-2002-22-2000000000000000000000000006−6−66−666−600000000000000000000000000
χ884-4-44-4-444-44-200-4400-2222-22-2002-22-200000000000000000000000000−666−66−6−6600000000000000000000000000
χ898-88-88i−8i−8i8i00-400000044-4−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8−8i8i8i−8i00-400000044-44i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000

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