Finite Group Databasebeta

← Group #11798456

Character table — Group #11798456

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1122222222222444444444444444488888888888881212121212121212121212121212121212121616161616162424242424242424244848487272144
order122334466668836666812121212242424242424226666121224242424242466121216161616484848484848484866666624668121224244121216168
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111
χ511111111111111111111111111111-1-1-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-111-1
χ611111111111111111111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-11
χ711111111111111111111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-111-1-1-1-1-1-1-11
χ811111111111111111111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-111111-1
χ922222222222-2-222222-22222-2-2-2-2-2-200000022-2-2-2-2-22222220000000000000000000000-200-2-2000000
χ1022222222222-2-222222-22222-2-2-2-2-2-200000022-2-2-2-2-2-2-2-2-2-2-2000000000000000000000020022000000
χ112222-12222-1222-1-1-1-1-12-122-122-1-12222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000000022-1-1-1-122-1-12-1-1-1-1000000
χ122222-12222-1222-1-1-1-1-12-122-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-2-2111100000000000022-1-1-1-1-2-211-21111000000
χ132222-12222-1222-1-1-1-1-12-122-122-1-122-2-21111-1-1-1-1-1-1-122-1-1-1-1000000000000-2-21111-2-211211-1-1000000
χ142222-12222-1222-1-1-1-1-12-122-122-1-122-2-21111-1-1-1-1-1-1-1-2-21111000000000000-2-2111122-1-1-2-1-111000000
χ152222-12222-12-2-2-1-1-1-1-1-2-122-1-2-211-2-200−i3−i3i3i3-1-11111122-1-1-1-100000000000000−i3−i3i3i300−i3i3-2−i3i311000000
χ162222-12222-12-2-2-1-1-1-1-1-2-122-1-2-211-2-200−i3−i3i3i3-1-111111-2-2111100000000000000−i3−i3i3i300i3−i32i3−i3-1-1000000
χ172222-12222-12-2-2-1-1-1-1-1-2-122-1-2-211-2-200i3i3−i3−i3-1-11111122-1-1-1-100000000000000i3i3−i3−i300i3−i3-2i3−i311000000
χ182222-12222-12-2-2-1-1-1-1-1-2-122-1-2-211-2-200i3i3−i3−i3-1-111111-2-2111100000000000000i3i3−i3−i300−i3i32−i3i3-1-1000000
χ19222-1222-1-12-122-12-1-1-122-1-12-1-122-1-1222222-1-12-1-1-1-10000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000002-1-1000
χ20222-1222-1-12-122-12-1-1-122-1-12-1-122-1-1222222-1-12-1-1-1-1000000-2-2-2-211111111-1-1-1-1-1-1000000000-211000
χ21222-1222-1-12-122-12-1-1-122-1-12-1-122-1-1-2-2-2-2-2-2-1-12-1-1-1-10000002222-1-1-1-1-1-1-1-1111111000000000-211000
χ22222-1222-1-12-122-12-1-1-122-1-12-1-122-1-1-2-2-2-2-2-2-1-12-1-1-1-1000000-2-2-2-2111111111111110000000002-1-1000
χ2322-2222-2-2-222222-2-2-22-2-2-2222222-2-2000000-22-222-2-20000000000000000000000002-2220-2-200000000
χ2422-2222-2-2-222222-2-2-22-2-2-2222222-2-2000000-22-222-2-2000000000000000000000000-22-2-202200000000
χ2522-2222-2-2-222-2-22-2-2-222-2-222-2-2-2-2222-22-22-2-222-2-2220000000000000000002-22-22-2000000000000000
χ2622-2222-2-2-222-2-22-2-2-222-2-222-2-2-2-222-22-22-22-222-2-222000000000000000000-22-22-22000000000000000
χ2722-222-22-2-222002-2-2-22022-2-20000000000002-2000002-222-2-222−2−22222−2−2−2−20000000000000000002−20
χ2822-222-22-2-222002-2-2-22022-2-20000000000002-2000002-222-2-2−2−222−2−2−2−22222000000000000000000−220
χ2922-222-22-2-222002-2-2-22022-2-20000000000002-200000-22-2-22222−2−22222−2−2−2−2000000000000000000−220
χ3022-222-22-2-222002-2-2-22022-2-20000000000002-200000-22-2-222−2−222−2−2−2−222220000000000000000002−20
χ3122-22-12-2-2-2-1222-1111-1-21-22-122-1-1-2-200−i3i3i3−i31-11-1-11100−i3i3−i3i300000000000000−i3i3i3−i32-2-1-1011−i3i3000000
χ3222-22-12-2-2-2-1222-1111-1-21-22-122-1-1-2-200−i3i3i3−i31-11-1-11100i3−i3i3−i300000000000000−i3i3i3−i3-22110-1-1i3−i3000000
χ3322-22-12-2-2-2-1222-1111-1-21-22-122-1-1-2-200i3−i3−i3i31-11-1-11100−i3i3−i3i300000000000000i3−i3−i3i3-22110-1-1−i3i3000000
χ3422-22-12-2-2-2-1222-1111-1-21-22-122-1-1-2-200i3−i3−i3i31-11-1-11100i3−i3i3−i300000000000000i3−i3−i3i32-2-1-1011i3−i3000000
χ3522-22-12-2-2-2-12-2-2-1111-121-22-1-2-211222-2-11-111-1-111-1-100−i3i3−i3i30000000000002-2-11-1100−i3i30i3−i3i3−i3000000
χ3622-22-12-2-2-2-12-2-2-1111-121-22-1-2-211222-2-11-111-1-111-1-100i3−i3i3−i30000000000002-2-11-1100i3−i30−i3i3−i3i3000000
χ3722-22-12-2-2-2-12-2-2-1111-121-22-1-2-21122-221-11-11-1-111-1-100−i3i3−i3i3000000000000-221-11-100i3−i30−i3i3i3−i3000000
χ3822-22-12-2-2-2-12-2-2-1111-121-22-1-2-21122-221-11-11-1-111-1-100i3−i3i3−i3000000000000-221-11-100−i3i30i3−i3−i3i3000000
χ3922-2-122-2112-1-2-2-1-211-12-21-1211-2-2-1-12-22-22-21-1211-1-10000000000−i3−i3i3i3−i3−i3i3i3-11-11-110000000000−i3i3000
χ4022-2-122-2112-1-2-2-1-211-12-21-1211-2-2-1-12-22-22-21-1211-1-10000000000i3i3−i3−i3i3i3−i3−i3-11-11-110000000000i3−i3000
χ4122-2-122-2112-1-2-2-1-211-12-21-1211-2-2-1-1-22-22-221-1211-1-10000000000−i3−i3i3i3−i3−i3i3i31-11-11-10000000000i3−i3000
χ4222-2-122-2112-1-2-2-1-211-12-21-1211-2-2-1-1-22-22-221-1211-1-10000000000i3i3−i3−i3i3i3−i3−i31-11-11-10000000000−i3i3000
χ4344444-4-4444400444440-4-4-4-4000000000000-4-400000000000000000000000000000000000000000000
χ444444-2-4-444-2400-2-2-2-2-202-4-42000000000000220000000−2i32i32i3−2i3000000000000000000000000000000000
χ454444-2-4-444-2400-2-2-2-2-202-4-420000000000002200000002i3−2i3−2i32i3000000000000000000000000000000000
χ46444-2444-2-24-2-4-4-24-2-2-2-44-2-2422-4-422000000-2-2-42222000000000000000000000000000000000000000
χ47444-24-4-4-2-24-200-24-2-2-20-422-400000000000022000000000000000i6i6−i6−i6−i6−i6i6i6000000000000000000000
χ48444-24-4-4-2-24-200-24-2-2-20-422-400000000000022000000000000000−i6−i6i6i6i6i6−i6−i6000000000000000000000
χ49444-2-244-2-2-2-2441-21114-2-2-2-2-2-2-2-2-2-244-2-2-2-211-21111000000000000000000-2-21111000000000000000
χ50444-2-244-2-2-2-2441-21114-2-2-2-2-2-2-2-2-2-2-4-4222211-2111100000000000000000022-1-1-1-1000000000000000
χ51444-2-244-2-2-2-2-4-41-2111-4-2-2-2-222222200−2i3−2i32i32i3112-1-1-1-100000000000000000000i3i3−i3−i3000000000000000
χ52444-2-244-2-2-2-2-4-41-2111-4-2-2-2-2222222002i32i3−2i3−2i3112-1-1-1-100000000000000000000−i3−i3i3i3000000000000000
χ5344-44-2-44-4-4-2400-2222-20-24-42000000000000-22000004-4-2-222000000000000000000000000000000000
χ5444-44-2-44-4-4-2400-2222-20-24-42000000000000-2200000-4422-2-2000000000000000000000000000000000
χ5544-4-244-4224-244-2-422-2-4-42-24-2-244220000002-2-4-2-222000000000000000000000000000000000000000
χ5644-4-24-44224-200-2-422-204-22-4000000000000-22000000000002222−22−22−2−2−2−22222000000000000000000000
χ5744-4-24-44224-200-2-422-204-22-4000000000000-2200000000000−22−2222222222−2−2−2−2000000000000000000000
χ5844-4-2-24-422-2-24412-1-11-422-2-2-2-2-2-22200−2i32i32i3−2i3-11211-1-100000000000000000000i3−i3−i3i3000000000000000
χ5944-4-2-24-422-2-24412-1-11-422-2-2-2-2-2-222002i3−2i3−2i32i3-11211-1-100000000000000000000−i3i3i3−i3000000000000000
χ6044-4-2-24-422-2-2-4-412-1-11422-2-22222-2-24-4-22-22-11-2-1-111000000000000000000-221-11-1000000000000000
χ6144-4-2-24-422-2-2-4-412-1-11422-2-22222-2-2-442-22-2-11-2-1-1110000000000000000002-2-11-11000000000000000
χ624-40440000-4-422−224000-40000022−2222−220000000000022−2200000000ζ11+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−ζ47ζ11+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+ζ47ζ11+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−ζ47000000000000000000000
χ634-40440000-4-422−224000-40000022−2222−220000000000022−2200000000−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+ζ47−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−ζ47−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+ζ47000000000000000000000
χ644-40440000-4-4−22224000-400000−2222−222200000000000−222200000000ζ11+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−ζ47ζ11+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−ζ47−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−ζ47000000000000000000000
χ654-40440000-4-4−22224000-400000−2222−222200000000000−222200000000−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+ζ47−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+ζ47ζ11+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+ζ47000000000000000000000
χ664-40-2400−2i32i3-4222−22-20−2i32i3200000−2222−22i6−i6000000000−22i6−i6000000ζ11+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−ζ47−ζ11+ζ25−ζ29+ζ31ζ11−ζ25+ζ29−ζ31−ζ13+ζ41−ζ43+ζ47ζ13−ζ41+ζ43−ζ47−ζ13−ζ41−ζ43−ζ47ζ13+ζ41+ζ43+ζ47−ζ11−ζ25−ζ29−ζ31ζ11+ζ25+ζ29+ζ31000000000000000000000
χ674-40-2400−2i32i3-4222−22-20−2i32i3200000−2222−22i6−i6000000000−22i6−i6000000−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+ζ47ζ11−ζ25+ζ29−ζ31−ζ11+ζ25−ζ29+ζ31ζ13−ζ41+ζ43−ζ47−ζ13+ζ41−ζ43+ζ47ζ13+ζ41+ζ43+ζ47−ζ13−ζ41−ζ43−ζ47ζ11+ζ25+ζ29+ζ31−ζ11−ζ25−ζ29−ζ31000000000000000000000
χ684-40-2400−2i32i3-42−2222-20−2i32i32000002−2−2222−i6i60000000002−2−i6i6000000ζ11+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−ζ47−ζ13−ζ41−ζ43−ζ47ζ13+ζ41+ζ43+ζ47−ζ11−ζ25−ζ29−ζ31ζ11+ζ25+ζ29+ζ31ζ11−ζ25+ζ29−ζ31−ζ11+ζ25−ζ29+ζ31ζ13−ζ41+ζ43−ζ47−ζ13+ζ41−ζ43+ζ47000000000000000000000
χ694-40-2400−2i32i3-42−2222-20−2i32i32000002−2−2222−i6i60000000002−2−i6i6000000−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+ζ47ζ13+ζ41+ζ43+ζ47−ζ13−ζ41−ζ43−ζ47ζ11+ζ25+ζ29+ζ31−ζ11−ζ25−ζ29−ζ31−ζ11+ζ25−ζ29+ζ31ζ11−ζ25+ζ29−ζ31−ζ13+ζ41−ζ43+ζ47ζ13−ζ41+ζ43−ζ47000000000000000000000
χ704-40-24002i3−2i3-4222−22-202i3−2i3200000−2222−22−i6i6000000000−22−i6i6000000ζ11+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−ζ47−ζ13+ζ41−ζ43+ζ47ζ13−ζ41+ζ43−ζ47−ζ11+ζ25−ζ29+ζ31ζ11−ζ25+ζ29−ζ31−ζ11−ζ25−ζ29−ζ31ζ11+ζ25+ζ29+ζ31−ζ13−ζ41−ζ43−ζ47ζ13+ζ41+ζ43+ζ47000000000000000000000
χ714-40-24002i3−2i3-4222−22-202i3−2i3200000−2222−22−i6i6000000000−22−i6i6000000−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+ζ47ζ13−ζ41+ζ43−ζ47−ζ13+ζ41−ζ43+ζ47ζ11−ζ25+ζ29−ζ31−ζ11+ζ25−ζ29+ζ31ζ11+ζ25+ζ29+ζ31−ζ11−ζ25−ζ29−ζ31ζ13+ζ41+ζ43+ζ47−ζ13−ζ41−ζ43−ζ47000000000000000000000
χ724-40-24002i3−2i3-42−2222-202i3−2i32000002−2−2222i6−i60000000002−2i6−i6000000ζ11+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−ζ47−ζ11−ζ25−ζ29−ζ31ζ11+ζ25+ζ29+ζ31−ζ13−ζ41−ζ43−ζ47ζ13+ζ41+ζ43+ζ47ζ13−ζ41+ζ43−ζ47−ζ13+ζ41−ζ43+ζ47ζ11−ζ25+ζ29−ζ31−ζ11+ζ25−ζ29+ζ31000000000000000000000
χ734-40-24002i3−2i3-42−2222-202i3−2i32000002−2−2222i6−i60000000002−2i6−i6000000−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+ζ47ζ11+ζ25+ζ29+ζ31−ζ11−ζ25−ζ29−ζ31ζ13+ζ41+ζ43+ζ47−ζ13−ζ41−ζ43−ζ47−ζ13+ζ41−ζ43+ζ47ζ13−ζ41+ζ43−ζ47−ζ11+ζ25−ζ29+ζ31ζ11−ζ25+ζ29−ζ31000000000000000000000
χ74888-4-4-8-8-4-4-4-4002-422204444000000000000-2-200000000000000000000000000000000000000000000
χ7588-8-4-4-8844-4-40024-2-220-4-4440000000000002-200000000000000000000000000000000000000000000
χ768-808-400004-842−42-400040000042−42−222200000000000−222200000000000000000000000000000000000000000
χ778-808-400004-8−4242-4000400000−424222−220000000000022−2200000000000000000000000000000000000000000
χ788-80-4-400−4i34i34442−42202i3−2i3-200000−2222−22222i6−2i60000000002−2−i6i6000000000000000000000000000000000000000
χ798-80-4-400−4i34i344−4242202i3−2i3-20000022−2222−22−2i62i6000000000−22i6−i6000000000000000000000000000000000000000
χ808-80-4-4004i3−4i34442−4220−2i32i3-200000−2222−2222−2i62i60000000002−2i6−i6000000000000000000000000000000000000000
χ818-80-4-4004i3−4i344−424220−2i32i3-20000022−2222−222i6−2i6000000000−22−i6i6000000000000000000000000000000000000000

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