Finite Group Databasebeta

← Group #10951985

Character table — Group #10951985

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11222222222224444444444444444446688888888888888881212121212121212121616161616161616161624242448484848
order122344688161616162466681212121216162424484848488822448161624242448484848484824448161616164466121212121212816162288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1
χ31111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111-1-11-1-111-1-1111111111111111-1-1-11-1-111-1-1-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-1-111
χ61111111111111-1-11-1-111-1-111111111111-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1111111111-1-1-1-11111-1-1-111-1-1
χ71111111111111-1-11-1-111-1-1111111111-1-11111-1-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1
χ81111111111111-1-11-1-111-1-1111111111-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-11111111-1-111
χ9111111111-1-1-1-11111111111-1-111-1-1-1-1111-11-11-1-1111-1-1-1-1-1-111111-1-1-1-11-11-11-111-1-11-1-11-11-1
χ10111111111-1-1-1-11111111111-1-111-1-1-1-111-11-111-1-1111-1-1-1-1-1-111111-1-1-1-1-11-11-11-1-1111-1-1-11-11
χ11111111111-1-1-1-11111111111-1-111-1-1-1-1-1-11-11-11-1-1111-1-1-1-1-1-1-1-1-1-1-111111-11-11-111-1-1-111-11-11
χ12111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-11-111-1-1111-1-1-1-1-1-1-1-1-1-1-11111-11-11-11-1-111-1111-11-1
χ13111111111-1-1-1-1-1-11-1-111-1-11-1-111-1-1-1-1111-11-1-1111-1-1-1-11111-1-1111-1-1-1-1-111-11-1-1-111-111-111-1
χ14111111111-1-1-1-1-1-11-1-111-1-11-1-111-1-1-1-111-11-11-1111-1-1-1-11111-1-1111-1-1-1-11-1-11-1111-1-1-1111-1-11
χ15111111111-1-1-1-1-1-11-1-111-1-11-1-111-1-1-1-1-1-11-11-1-1111-1-1-1-1111111-1-1-11111-111-11-1-1-1111-1-11-1-11
χ16111111111-1-1-1-1-1-11-1-111-1-11-1-111-1-1-1-1-1-1-11-11-1111-1-1-1-1111111-1-1-111111-1-11-1111-1-11-1-1-111-1
χ172222222-2-2000022222-2222200-2-20000220000-200-2-2-200000022-2-2200000000000000-2000000
χ182222222-2-2000022222-2222200-2-20000-2-20000-200-2-2-2000000-2-222-2000000000000002000000
χ192222222-2-20000-2-22-2-2-22-2-2200-2-20000220000200-222000000-2-2-2-22000000000000002000000
χ202222222-2-20000-2-22-2-2-22-2-2200-2-20000-2-20000200-2220000002222-200000000000000-2000000
χ21222-122-122222222-1-1-12-1-1-1-122-1-1-1-1-1-1002222222-1-1-1-1-1-1-1-1-100000000022-1-1-1-1-1-1-1-10000000
χ22222-122-122222222-1-1-12-1-1-1-122-1-1-1-1-1-100-2-2-2-2222-1-1-1-1-1-1-1-1-1000000000-2-2111111110000000
χ23222-122-1222222-2-2-1112-111-122-1-1-1-1-1-1002222-2-2-2-111-1-11111000000000-2-2-1-1-1-111110000000
χ24222-122-1222222-2-2-1112-111-122-1-1-1-1-1-100-2-2-2-2-2-2-2-111-1-11111000000000221111-1-1-1-10000000
χ25222-122-122-2-2-2-222-1-1-12-1-1-1-1-2-2-1-11111002-22-22-2-2-1-1-11111110000000002-2-11-11-1-1110000000
χ26222-122-122-2-2-2-222-1-1-12-1-1-1-1-2-2-1-1111100-22-222-2-2-1-1-1111111000000000-221-11-111-1-10000000
χ27222-122-122-2-2-2-2-2-2-1112-111-1-2-2-1-11111002-22-2-222-11111-1-1-1-1000000000-22-11-1111-1-10000000
χ28222-122-122-2-2-2-2-2-2-1112-111-1-2-2-1-1111100-22-22-222-11111-1-1-1-10000000002-21-11-1-1-1110000000
χ2922-222-2222222200-200-2-2002-2-22222220022-2-2000-200-2-200000000000000022-2-200000000000
χ3022-222-2222222200-200-2-2002-2-222222200-2-222000-200-2-2000000000000000-2-22200000000000
χ3122-222-2222-2-2-2-200-200-2-20022222-2-2-2-2002-2-22000-200220000000000000002-2-2200000000000
χ3222-222-2222-2-2-2-200-200-2-20022222-2-2-2-200-222-2000-20022000000000000000-222-200000000000
χ3322-22-2220022−2−22-2-22202-2-2-22−20022−2−222000002−20002−222−2−2-2200-222−2−2000000000002−20000
χ3422-22-2220022−2−22-2-22202-2-2-22−20022−2−2-2-2000002−20002−222−2−22-2002−2−22200000000000−220000
χ3522-22-2220022−2−2-22-2-2-20222-22−20022−2−22200000−220002−2−2−2222-200-222−2−200000000000−220000
χ3622-22-2220022−2−2-22-2-2-20222-22−20022−2−2-2-200000−220002−2−2−222-22002−2−222000000000002−20000
χ3722-22-22200−2−2222-2-22202-2-2-2−2200−2−2222200000−22000−22−2−222-2200-2−2−22200000000000−220000
χ3822-22-22200−2−2222-2-22202-2-2-2−2200−2−222-2-200000−22000−22−2−2222-200222−2−2000000000002−20000
χ3922-22-22200−2−222-22-2-2-20222-2−2200−2−22222000002−2000−2222−2−22-200-2−2−222000000000002−20000
χ4022-22-22200−2−222-22-2-2-20222-2−2200−2−222-2-2000002−2000−2222−2−2-2200222−2−200000000000−220000
χ4122-2-12-2-1222222001−i3i3-21−i3i3-1-2-2-1-1-1-1-1-10022-2-20001−i3i311−i3i3−i3i300000000000-1-111−i3i3−i3i30000000
χ4222-2-12-2-1222222001−i3i3-21−i3i3-1-2-2-1-1-1-1-1-100-2-2220001−i3i311−i3i3−i3i30000000000011-1-1i3−i3i3−i30000000
χ4322-2-12-2-1222222001i3−i3-21i3−i3-1-2-2-1-1-1-1-1-10022-2-20001i3−i311i3−i3i3−i300000000000-1-111i3−i3i3−i30000000
χ4422-2-12-2-1222222001i3−i3-21i3−i3-1-2-2-1-1-1-1-1-100-2-2220001i3−i311i3−i3i3−i30000000000011-1-1−i3i3−i3i30000000
χ4522-2-12-2-122-2-2-2-2001−i3i3-21−i3i3-122-1-11111002-2-220001−i3i3-1-1i3−i3i3−i300000000000-111-1−i3i3i3−i30000000
χ4622-2-12-2-122-2-2-2-2001−i3i3-21−i3i3-122-1-1111100-222-20001−i3i3-1-1i3−i3i3−i3000000000001-1-11i3−i3−i3i30000000
χ4722-2-12-2-122-2-2-2-2001i3−i3-21i3−i3-122-1-11111002-2-220001i3−i3-1-1−i3i3−i3i300000000000-111-1i3−i3−i3i30000000
χ4822-2-12-2-122-2-2-2-2001i3−i3-21i3−i3-122-1-1111100-222-20001i3−i3-1-1−i3i3−i3i3000000000001-1-11−i3i3i3−i30000000
χ494444-4-44002222−22−22004000-400-4−2222002222−22−22000000000000−2222000000000000000000000000000000
χ504444-4-4400−22−222222004000-400-422−2200−22−22222200000000000022−22000000000000000000000000000000
χ51444-244-2-4-4000044-2-2-2-4-2-2-2-200220000000000-40022200000000000000000000000000000000
χ52444-244-2-4-40000-4-4-222-4-222-2002200000000004002-2-200000000000000000000000000000000
χ53444-2-4-4-2002222−22−2200-2−2i32i3022i3−2i32−222200−2−2220000000000002−2−i6i6i6−i600000000000000000000000000
χ54444-2-4-4-2002222−22−2200-22i3−2i302−2i32i32−222200−2−2220000000000002−2i6−i6−i6i600000000000000000000000000
χ55444-2-4-4-200−22−22222200-2−2i32i3022i3−2i3222−220022−2−2000000000000−22i6−i6−i6i600000000000000000000000000
χ56444-2-4-4-200−22−22222200-22i3−2i302−2i32i3222−220022−2−2000000000000−22−i6i6i6−i600000000000000000000000000
χ5744-444-44-4-4000000-4004-400400-4-4000000000000040000000000000000000000000000000000
χ5844-4-24-4-2-4-40000002−2i32i342−2i32i3-200220000000000000-22i3−2i300000000000000000000000000000000
χ5944-4-24-4-2-4-400000022i3−2i3422i3−2i3-200220000000000000-2−2i32i300000000000000000000000000000000
χ6044-4-2-44-2002222−22−224-42-2-20-222222−2200−2−222000000022−22000−22−2−22200000000000000000000000000
χ6144-4-2-44-2002222−22−22-442220-2-2-2222−2200−2−2220000000−2222000−2222−2−200000000000000000000000000
χ6244-4-2-44-200−22−2222224-42-2-20-2222−22220022−2−20000000−22220002−222−2−200000000000000000000000000
χ6344-4-2-44-200−22−222222-442220-2-2-22−22220022−2−2000000022−220002−2−2−22200000000000000000000000000
χ644-40400-422−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ4300000000000022−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ43−2i22i20000000000000000002i−2i0ζ11+ζ13+ζ25+ζ29+ζ31+ζ41+ζ43+ζ47−ζ11−ζ13−ζ25−ζ29−ζ31−ζ41−ζ43−ζ47ζ11+ζ13−ζ25+ζ29−ζ31−ζ41+ζ43−ζ47−ζ11−ζ13+ζ25−ζ29+ζ31+ζ41−ζ43+ζ4700000000000000000
χ654-40400-422−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ4300000000000022−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432i2−2i2000000000000000000−2i2i0−ζ11−ζ13−ζ25−ζ29−ζ31−ζ41−ζ43−ζ47ζ11+ζ13+ζ25+ζ29+ζ31+ζ41+ζ43+ζ47−ζ11−ζ13+ζ25−ζ29+ζ31+ζ41−ζ43+ζ47ζ11+ζ13−ζ25+ζ29−ζ31−ζ41+ζ43−ζ4700000000000000000
χ664-40400-422−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ4300000000000022−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2i22i20000000000000000002i−2i0−ζ11−ζ13−ζ25−ζ29−ζ31−ζ41−ζ43−ζ47ζ11+ζ13+ζ25+ζ29+ζ31+ζ41+ζ43+ζ47−ζ11−ζ13+ζ25−ζ29+ζ31+ζ41−ζ43+ζ47ζ11+ζ13−ζ25+ζ29−ζ31−ζ41+ζ43−ζ4700000000000000000
χ674-40400-422−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ4300000000000022−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ432i2−2i2000000000000000000−2i2i0ζ11+ζ13+ζ25+ζ29+ζ31+ζ41+ζ43+ζ47−ζ11−ζ13−ζ25−ζ29−ζ31−ζ41−ζ43−ζ47ζ11+ζ13−ζ25+ζ29−ζ31−ζ41+ζ43−ζ47−ζ11−ζ13+ζ25−ζ29+ζ31+ζ41−ζ43+ζ4700000000000000000
χ684-40400-4−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47000000000000−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2i22i2000000000000000000−2i2i0−ζ11−ζ13+ζ25−ζ29+ζ31+ζ41−ζ43+ζ47ζ11+ζ13−ζ25+ζ29−ζ31−ζ41+ζ43−ζ47ζ11+ζ13+ζ25+ζ29+ζ31+ζ41+ζ43+ζ47−ζ11−ζ13−ζ25−ζ29−ζ31−ζ41−ζ43−ζ4700000000000000000
χ694-40400-4−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47000000000000−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472i2−2i20000000000000000002i−2i0ζ11+ζ13−ζ25+ζ29−ζ31−ζ41+ζ43−ζ47−ζ11−ζ13+ζ25−ζ29+ζ31+ζ41−ζ43+ζ47−ζ11−ζ13−ζ25−ζ29−ζ31−ζ41−ζ43−ζ47ζ11+ζ13+ζ25+ζ29+ζ31+ζ41+ζ43+ζ4700000000000000000
χ704-40400-4−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47000000000000−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2i22i2000000000000000000−2i2i0ζ11+ζ13−ζ25+ζ29−ζ31−ζ41+ζ43−ζ47−ζ11−ζ13+ζ25−ζ29+ζ31+ζ41−ζ43+ζ47−ζ11−ζ13−ζ25−ζ29−ζ31−ζ41−ζ43−ζ47ζ11+ζ13+ζ25+ζ29+ζ31+ζ41+ζ43+ζ4700000000000000000
χ714-40400-4−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47000000000000−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472i2−2i20000000000000000002i−2i0−ζ11−ζ13+ζ25−ζ29+ζ31+ζ41−ζ43+ζ47ζ11+ζ13−ζ25+ζ29−ζ31−ζ41+ζ43−ζ47ζ11+ζ13+ζ25+ζ29+ζ31+ζ41+ζ43+ζ47−ζ11−ζ13−ζ25−ζ29−ζ31−ζ41−ζ43−ζ4700000000000000000
χ728-80-400442−42−4ζ25+4ζ31−4ζ41+4ζ474ζ25−4ζ31+4ζ41−4ζ474ζ11−4ζ13−4ζ29+4ζ43−4ζ11+4ζ13+4ζ29−4ζ43000000000000−22222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ4300000000000000000000000000000000000000000000
χ738-80-400442−424ζ25−4ζ31+4ζ41−4ζ47−4ζ25+4ζ31−4ζ41+4ζ47−4ζ11+4ζ13+4ζ29−4ζ434ζ11−4ζ13−4ζ29+4ζ43000000000000−2222−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ4300000000000000000000000000000000000000000000
χ748-80-4004−42424ζ11−4ζ13−4ζ29+4ζ43−4ζ11+4ζ13+4ζ29−4ζ434ζ25−4ζ31+4ζ41−4ζ47−4ζ25+4ζ31−4ζ41+4ζ4700000000000022−22−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ4700000000000000000000000000000000000000000000
χ758-80-4004−4242−4ζ11+4ζ13+4ζ29−4ζ434ζ11−4ζ13−4ζ29+4ζ43−4ζ25+4ζ31−4ζ41+4ζ474ζ25−4ζ31+4ζ41−4ζ4700000000000022−222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ4700000000000000000000000000000000000000000000

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