Finite Group Databasebeta

← Group #10713605

Character table — Group #10713605

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222222222224444444444444444444466666666888888888812121212121212121212121216161616161616161616161648484848
order1222223444466688884444668888881212121224242424161616161616161612121212242424242424161616161616161616161616448812121212242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91-1-111-1111-1-1-1-1111-1-1ii−i−i1-11-1ii−i−i11-1-111-1-11111-1-1-1-1ii−i−i1-1ii−i−i11-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1-1i−i
χ101-1-111-1111-1-1-1-1111-1-1ii−i−i1-11-1ii−i−i11-1-111-1-11111-1-1-1-1ii−i−i1-1ii−i−i11-1-1iiii−i−i−i−i-11−ii-1-111−i−iii-11−ii
χ111-1-111-1111-1-1-1-1111-1-1ii−i−i1-11-1ii−i−i11-1-111-1-1-1-1-1-11111ii−i−i1-1ii−i−i-1-111−i−i−i−iiiii1-1i−i11-1-1ii−i−i-11−ii
χ121-1-111-1111-1-1-1-1111-1-1ii−i−i1-11-1ii−i−i11-1-111-1-1-1-1-1-11111ii−i−i1-1ii−i−i-1-111−i−i−i−iiiii-11−ii-1-111−i−iii1-1i−i
χ131-1-111-1111-1-1-1-1111-1-1−i−iii1-11-1−i−iii11-1-111-1-11111-1-1-1-1−i−iii1-1−i−iii11-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1-1−ii
χ141-1-111-1111-1-1-1-1111-1-1−i−iii1-11-1−i−iii11-1-111-1-11111-1-1-1-1−i−iii1-1−i−iii11-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i-11i−i
χ151-1-111-1111-1-1-1-1111-1-1−i−iii1-11-1−i−iii11-1-111-1-1-1-1-1-11111−i−iii1-1−i−iii-1-111iiii−i−i−i−i1-1−ii11-1-1−i−iii-11i−i
χ161-1-111-1111-1-1-1-1111-1-1−i−iii1-11-1−i−iii11-1-111-1-1-1-1-1-11111−i−iii1-1−i−iii-1-111iiii−i−i−i−i-11i−i-1-111ii−i−i1-1−ii
χ1722222222222222-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-2000000002222-2-2-2-2-2-20000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-222-2-222222222-2-2-2-200000000-2-2-2-2-2-222220000000000000000000000000000
χ192222222-2-2-2-22220000000022002i−2i2i−2i-2-2-2-2000022−2−222−2−20000002i−2i2i−2i2−22−2−i2−i2i2i2−i2−i2i2i20000000000000000
χ202222222-2-2-2-22220000000022002i−2i2i−2i-2-2-2-20000−2−222−2−2220000002i−2i2i−2i−22−22i2i2−i2−i2i2i2−i2−i20000000000000000
χ212222222-2-2-2-2222000000002200−2i2i−2i2i-2-2-2-2000022−2−222−2−2000000−2i2i−2i2i2−22−2i2i2−i2−i2i2i2−i2−i20000000000000000
χ222222222-2-2-2-2222000000002200−2i2i−2i2i-2-2-2-20000−2−222−2−222000000−2i2i−2i2i−22−22−i2−i2i2i2−i2−i2i2i20000000000000000
χ23222222-12222-1-1-122222222-1-1222222-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-10000000000002222-1-1-1-1-1-1-1-10000
χ24222222-12222-1-1-122222222-1-1222222-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-2111111110000
χ25222222-12222-1-1-12222-2-2-2-2-1-122-2-2-2-2-1-1-1-1-1-1-1-1000000001111-1-1111100000000000022-2-2-1-1-1-111110000
χ26222222-12222-1-1-12222-2-2-2-2-1-122-2-2-2-2-1-1-1-1-1-1-1-1000000001111-1-11111000000000000-2-2221111-1-1-1-10000
χ27222222-12222-1-1-1-2-2-2-22222-1-1-2-2-2-2-2-2-1-1-1-1111100000000-1-1-1-11111110000000000000000−i3i3−i3i3−i3i3−i3i30000
χ28222222-12222-1-1-1-2-2-2-22222-1-1-2-2-2-2-2-2-1-1-1-1111100000000-1-1-1-11111110000000000000000i3−i3i3−i3i3−i3i3−i30000
χ29222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-2-22222-1-1-1-1111100000000111111-1-1-1-10000000000000000−i3i3−i3i3i3−i3i3−i30000
χ30222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-2-22222-1-1-1-1111100000000111111-1-1-1-10000000000000000i3−i3i3−i3−i3i3−i3i30000
χ312222-2-222-2-2222200002-22-2-2-20000002-2-22000022−2−222−2−22-22-2000000−22−222−22−22−22−20000000000000000
χ322222-2-222-2-2222200002-22-2-2-20000002-2-220000−2−222−2−2222-22-20000002−22−2−22−22−22−220000000000000000
χ332222-2-222-2-222220000-22-22-2-20000002-2-22000022−2−222−2−2-22-22000000−22−22−22−22−22−220000000000000000
χ342222-2-222-2-222220000-22-22-2-20000002-2-220000−2−222−2−222-22-220000002−22−22−22−22−22−20000000000000000
χ352222-2-22-222-222222220000-2-2-2-20000-222-22222222222220000-2-20000-2-2-2-2000000000000000000000000
χ362222-2-22-222-222222220000-2-2-2-20000-222-22222-2-2-2-2-2-2-2-20000-2-200002222000000000000000000000000
χ372222-2-22-222-2222-2-2-2-20000-2-2220000-222-2-2-2-2-200000000000022000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ382222-2-22-222-2222-2-2-2-20000-2-2220000-222-2-2-2-2-20000000000002200000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ392-2-222-2222-2-2-2-22-2-2222i2i−2i−2i2-2-22−2i−2i2i2i22-2-2-2-222000000002i2i−2i−2i-22−2i−2i2i2i0000000000000000000000000000
χ402-2-222-2222-2-2-2-22-2-222−2i−2i2i2i2-2-222i2i−2i−2i22-2-2-2-22200000000−2i−2i2i2i-222i2i−2i−2i0000000000000000000000000000
χ412-2-222-22-2-222-2-22000000002-2002-2-22-2-222000022−2−2−2−2220000002-2-222−2−22−2−22222−2−20000000000000000
χ422-2-222-22-2-222-2-22000000002-2002-2-22-2-2220000−2−22222−2−20000002-2-22−222−222−2−2−2−2220000000000000000
χ432-2-222-22-2-222-2-22000000002-200-222-2-2-222000022−2−2−2−222000000-222-22−2−2222−2−2−2−2220000000000000000
χ442-2-222-22-2-222-2-22000000002-200-222-2-2-2220000−2−22222−2−2000000-222-2−222−2−2−22222−2−20000000000000000
χ452-2-222-2-122-2-211-122-2-22i2i−2i−2i-112-22i2i−2i−2i-1-111-1-11100000000−i−iii-11−i−iii0000000000002-22i−2i-1-111−i−iii0000
χ462-2-222-2-122-2-211-122-2-22i2i−2i−2i-112-22i2i−2i−2i-1-111-1-11100000000−i−iii-11−i−iii000000000000-22−2i2i11-1-1ii−i−i0000
χ472-2-222-2-122-2-211-122-2-2−2i−2i2i2i-112-2−2i−2i2i2i-1-111-1-11100000000ii−i−i-11ii−i−i0000000000002-2−2i2i-1-111ii−i−i0000
χ482-2-222-2-122-2-211-122-2-2−2i−2i2i2i-112-2−2i−2i2i2i-1-111-1-11100000000ii−i−i-11ii−i−i000000000000-222i−2i11-1-1−i−iii0000
χ492-2-222-2-122-2-211-1-2-2222i2i−2i−2i-11-22−2i−2i2i2i-1-11111-1-100000000−i−iii1-1ii−i−i0000000000000000−i3i3i3−i33−3−330000
χ502-2-222-2-122-2-211-1-2-2222i2i−2i−2i-11-22−2i−2i2i2i-1-11111-1-100000000−i−iii1-1ii−i−i0000000000000000i3−i3−i3i3−333−30000
χ512-2-222-2-122-2-211-1-2-222−2i−2i2i2i-11-222i2i−2i−2i-1-11111-1-100000000ii−i−i1-1−i−iii0000000000000000−i3i3i3−i3−333−30000
χ522-2-222-2-122-2-211-1-2-222−2i−2i2i2i-11-222i2i−2i−2i-1-11111-1-100000000ii−i−i1-1−i−iii0000000000000000i3−i3−i3i33−3−330000
χ532-2-22-2222-22-2-2-2200002i−2i−2i2i-220000002-22-2000022−2−2−2−2222i−2i−2i2i000000−222−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ542-2-22-2222-22-2-2-2200002i−2i−2i2i-220000002-22-20000−2−22222−2−22i−2i−2i2i0000002−2−22−i2i2−i2i2i2−i2i2−i20000000000000000
χ552-2-22-2222-22-2-2-220000−2i2i2i−2i-220000002-22-2000022−2−2−2−222−2i2i2i−2i000000−222−2−i2i2−i2i2i2−i2i2−i20000000000000000
χ562-2-22-2222-22-2-2-220000−2i2i2i−2i-220000002-22-20000−2−22222−2−2−2i2i2i−2i0000002−2−22i2−i2i2−i2−i2i2−i2i20000000000000000
χ572-2-22-222-22-22-2-2222-2-20000-22-220000-22-2222-2-22222-2-2-2-20000-220000-2-222000000000000000000000000
χ582-2-22-222-22-22-2-2222-2-20000-22-220000-22-2222-2-2-2-2-2-222220000-22000022-2-2000000000000000000000000
χ592-2-22-222-22-22-2-22-2-2220000-222-20000-22-22-2-2220000000000002-2000000002-2-22-222-20000000000000000
χ602-2-22-222-22-22-2-22-2-2220000-222-20000-22-22-2-2220000000000002-200000000-222-22-2-220000000000000000
χ61444444-2-4-4-4-4-2-2-200000000-2-2004i−4i4i−4i2222000000000000000000−2i2i−2i2i0000000000000000000000000000
χ62444444-2-4-4-4-4-2-2-200000000-2-200−4i4i−4i4i22220000000000000000002i−2i2i−2i0000000000000000000000000000
χ634444-4-4-24-4-44-2-2-200004-44-422000000-222-2000000000000-22-220000000000000000000000000000000000
χ644444-4-4-24-4-44-2-2-20000-44-4422000000-222-20000000000002-22-20000000000000000000000000000000000
χ654444-4-4-2-444-4-2-2-24444000022-4-400002-2-22-2-2-2-20000000000002200000000000000000000000000000000
χ664444-4-4-2-444-4-2-2-2-4-4-4-40000224400002-2-222222000000000000-2-200000000000000000000000000000000
χ6744-4-400400004-4-422−2222−22000000000000000022−2222−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ4300000000000000000000000000000000000000
χ6844-4-400400004-4-422−2222−22000000000000000022−2222−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ4300000000000000000000000000000000000000
χ6944-4-400400004-4-4−2222−22220000000000000000−2222−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ4700000000000000000000000000000000000000
χ7044-4-400400004-4-4−2222−22220000000000000000−2222−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ4700000000000000000000000000000000000000
χ714-44-40040000-44-422−22−2222000000000000000022−22−2222−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ4300000000000000000000000000000000000000
χ724-44-40040000-44-422−22−2222000000000000000022−22−22222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ4300000000000000000000000000000000000000
χ734-44-40040000-44-4−222222−220000000000000000−222222−222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ4700000000000000000000000000000000000000
χ744-44-40040000-44-4−222222−220000000000000000−222222−22−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ4700000000000000000000000000000000000000
χ754-4-444-4-2-4-44422-200000000-22004-4-4422-2-2000000000000000000-222-20000000000000000000000000000
χ764-4-444-4-2-4-44422-200000000-2200-444-422-2-20000000000000000002-2-220000000000000000000000000000
χ774-4-44-44-24-44-422-200004i−4i−4i4i2-2000000-22-22000000000000−2i2i2i−2i0000000000000000000000000000000000
χ784-4-44-44-24-44-422-20000−4i4i4i−4i2-2000000-22-220000000000002i−2i−2i2i0000000000000000000000000000000000
χ794-4-44-44-2-44-4422-244-4-400002-2-4400002-22-2-2-2220000000000002-200000000000000000000000000000000
χ804-4-44-44-2-44-4422-2-4-44400002-24-400002-22-222-2-2000000000000-2200000000000000000000000000000000
χ8188-8-800-40000-44442−4242−420000000000000000−2222−22220000000000000000000000000000000000000000000000
χ8288-8-800-40000-444−4242−4242000000000000000022−2222−220000000000000000000000000000000000000000000000
χ838-88-800-400004-4442−42−42420000000000000000−222222−220000000000000000000000000000000000000000000000
χ848-88-800-400004-44−424242−42000000000000000022−22−22220000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.