Finite Group Databasebeta

← Group #11799788

Character table — Group #11799788

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size111122222222222222444444444444444466888888121212121212121212121212121212121212121212121216161616161616161624243636363648484848487272
order12223344666666888836661212121224242424242424242212122424242446688121216161616242424244848484848484848412121212121212124416161616266121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1111-1-1-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-11111-1-1-1-11111111111111111111-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111
χ71111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11111-1-1-1-1-111
χ81111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1
χ922222222222222-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-2222-2-2220000-2-2-2-2000000000000000000000000000000
χ1022222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-222-2-200002222000000000000000000000000000000
χ11222222-2-222222200002222-2-2-2-20000000022-2-20000-22200-2-222−2−200002222−2−2−2−20000000000022−2−20000000
χ12222222-2-222222200002222-2-2-2-20000000022-2-20000-22200-2-2−2−2220000−2−2−2−2222200000000000−2−2220000000
χ13222222-2-222222200002222-2-2-2-200000000-2-2-2-200002-2-2002222−2−200002222−2−2−2−200000000000−2−2220000000
χ14222222-2-222222200002222-2-2-2-200000000-2-2-2-200002-2-20022−2−2220000−2−2−2−222220000000000022−2−20000000
χ1522222-1222-12-1-122222-1-1-1-12-12-122-1-1-1-12222-1-1-1-1-1-12-1-122-1-10000-1-1-1-1000000002-1-122-1-1-1-10000002-1-10000
χ1622222-1222-12-1-122222-1-1-1-12-12-122-1-1-1-12222-1-1-1-1-1-12-1-122-1-10000-1-1-1-100000000-211-2-21111000000-2110000
χ1722222-1222-12-1-122222-1-1-1-12-12-122-1-1-1-122-2-2-1-1-1-1-1-1-211-2-21100001111000000002-1-122-1-1-1-1000000-2110000
χ1822222-1222-12-1-122222-1-1-1-12-12-122-1-1-1-122-2-2-1-1-1-1-1-1-211-2-2110000111100000000-211-2-211110000002-1-10000
χ1922222-1222-12-1-12-2-2-2-2-1-1-1-12-12-1-2-21111-2-222-1-111112-1-1-2-2-1-100001111000000000−i3i300−i3−i3i3i30000000−i3i30000
χ2022222-1222-12-1-12-2-2-2-2-1-1-1-12-12-1-2-21111-2-222-1-111112-1-1-2-2-1-100001111000000000i3−i300i3i3−i3−i30000000i3−i30000
χ2122222-1222-12-1-12-2-2-2-2-1-1-1-12-12-1-2-21111-2-2-2-2-1-11111-21122110000-1-1-1-1000000000−i3i300−i3−i3i3i30000000i3−i30000
χ2222222-1222-12-1-12-2-2-2-2-1-1-1-12-12-1-2-21111-2-2-2-2-1-11111-21122110000-1-1-1-1000000000i3−i300i3i3−i3−i30000000−i3i30000
χ232222-1222-12-122-12222-1-1-1-1-12-12-1-12222-1-100-1-1-1-1-1-1000000022220000-1-1-1-1-1-1-1-1222-1-1-1-1-1-1220000000-1-100
χ242222-1222-12-122-12222-1-1-1-1-12-12-1-12222-1-100-1-1-1-1-1-1000000022220000-1-1-1-1-1-1-1-1-2-2-2111111-2-200000001100
χ252222-1222-12-122-12222-1-1-1-1-12-12-1-12222-1-100-1-1-1-1-1-10000000-2-2-2-2000011111111222-1-1-1-1-1-1-2-200000001100
χ262222-1222-12-122-12222-1-1-1-1-12-12-1-12222-1-100-1-1-1-1-1-10000000-2-2-2-2000011111111-2-2-2111111220000000-1-100
χ272-22-222-22-2-222-2-222-2-22-22-2-2-222-2-222-2-22200-2222-2-2000000000000000000000000000000002i−2i00000002i−2i00
χ282-22-222-22-2-222-2-222-2-22-22-2-2-222-2-222-2-22200-2222-2-200000000000000000000000000000000−2i2i0000000−2i2i00
χ292-22-222-22-2-222-2-2-2-2222-22-2-2-22222-2-222-2-200-22-2-22200000000000000000000000000000000000000000002i−2i
χ302-22-222-22-2-222-2-2-2-2222-22-2-2-22222-2-222-2-200-22-2-2220000000000000000000000000000000000000000000−2i2i
χ312-22-2-12-221-2-12-2122-2-2-11-111-2-121122-2-2-1-1001-1-1-111000000000000000−i3−i3i3i3−i3−i3i3i30003−33−33−32i−2i0000000−ii00
χ322-22-2-12-221-2-12-2122-2-2-11-111-2-121122-2-2-1-1001-1-1-111000000000000000−i3−i3i3i3−i3−i3i3i3000−33−33−33−2i2i0000000i−i00
χ332-22-2-12-221-2-12-2122-2-2-11-111-2-121122-2-2-1-1001-1-1-111000000000000000i3i3−i3−i3i3i3−i3−i30003−33−33−3−2i2i0000000i−i00
χ342-22-2-12-221-2-12-2122-2-2-11-111-2-121122-2-2-1-1001-1-1-111000000000000000i3i3−i3−i3i3i3−i3−i3000−33−33−332i−2i0000000−ii00
χ352-2-222200-2-2-2-2222−22−22-2-2200002−22−22−22−22-2002−22−202-22−200−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ4322−2−2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ4300000000000−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000000
χ362-2-222200-2-2-2-2222−22−22-2-2200002−22−22−22−22-2002−22−202-22−200ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ4322−2−2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ4300000000000ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430000000
χ372-2-222200-2-2-2-2222−22−22-2-2200002−22−22−22−2-22002−22−20-22−2200−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−2−222−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ4300000000000ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430000000
χ382-2-222200-2-2-2-2222−22−22-2-2200002−22−22−22−2-22002−22−20-22−2200ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−2−222ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ4300000000000−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000000
χ392-2-222200-2-2-2-222−22−222-2-220000−22−22−22−222-200−22−2202-2−2200ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−2−222ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ4700000000000ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000000
χ402-2-222200-2-2-2-222−22−222-2-220000−22−22−22−222-200−22−2202-2−2200−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−2−222−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ4700000000000−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000000
χ412-2-222200-2-2-2-222−22−222-2-220000−22−22−22−22-2200−22−220-222−200ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ4722−2−2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ4700000000000−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000000
χ422-2-222200-2-2-2-222−22−222-2-220000−22−22−22−22-2200−22−220-222−200−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ4722−2−2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ4700000000000ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000000
χ4344444-2-4-44-24-2-240000-2-2-2-2-42-420000000044220000-4-2-2002200000000000000000000000000000000000000
χ4444444-2-4-44-24-2-240000-2-2-2-2-42-4200000000-4-422000042200-2-200000000000000000000000000000000000000
χ454444-2444-24-244-2-4-4-4-4-2-2-2-2-24-2422-4-4-4-42200-2-22222000000000000000000000000000000000000000000000
χ464444-24-4-4-24-244-20000-2-2-2-22-42-4000000000022000000000002222−22−220000−2−2−2−222220000000000000000000000
χ474444-24-4-4-24-244-20000-2-2-2-22-42-400000000002200000000000−22−22222200002222−2−2−2−20000000000000000000000
χ484444-2-244-2-2-2-2-2-244441111-2-2-2-2-2-2-2-2-2-2-2-200111111000000000000000000000004-2-2-2-211110000000000000
χ494444-2-244-2-2-2-2-2-244441111-2-2-2-2-2-2-2-2-2-2-2-20011111100000000000000000000000-42222-1-1-1-10000000000000
χ504444-2-244-2-2-2-2-2-2-4-4-4-41111-2-2-2-2222222220011-1-1-1-1000000000000000000000000−2i32i300i3i3−i3−i30000000000000
χ514444-2-244-2-2-2-2-2-2-4-4-4-41111-2-2-2-2222222220011-1-1-1-10000000000000000000000002i3−2i300−i3−i3i3i30000000000000
χ5244-4-4440044-4-4-4-422−22−222244-4-40000−222222−22−222222−22000022−22−2222000000000000000000000000000000000000000000000
χ5344-4-4440044-4-4-4-4−222222−2244-4-4000022−22−222222−22−22220000−222222−22000000000000000000000000000000000000000000000
χ5444-4-44-2004-2-422-422−22−2222-2-2220000−2222−222−222−220000−222−20000023−2300006−66−6000000000000000000000000000000
χ5544-4-44-2004-2-422-422−22−2222-2-2220000−2222−222−222−220000−222−200000−23230000−66−66000000000000000000000000000000
χ5644-4-44-2004-2-422-4−222222−22-2-222000022−222−2−22−222200002−2−220000023−230000−66−66000000000000000000000000000000
χ5744-4-44-2004-2-422-4−222222−22-2-222000022−222−2−22−222200002−2−2200000−232300006−66−6000000000000000000000000000000
χ5844-4-4-2400-242-4-4222−22−2222-2-22200002−222−22−2222−220000−222−2000000000000000−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ430000000000000000000000
χ5944-4-4-2400-242-4-4222−22−2222-2-22200002−222−22−2222−220000−222−2000000000000000ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ430000000000000000000000
χ6044-4-4-2400-242-4-42−222222−22-2-2220000−22−222222−222−200002−2−22000000000000000−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ470000000000000000000000
χ6144-4-4-2400-242-4-42−222222−22-2-2220000−22−222222−222−200002−2−22000000000000000ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ470000000000000000000000
χ624-44-4444-4-4-444-4-400004-44-444-4-400000000004-40000000000000000000000000000000000000000000000000
χ634-44-44-24-4-424-22-40000-22-224-2-420000000000-2200000000000000023−23−2323000000000000000000000000000000
χ644-44-44-24-4-424-22-40000-22-224-2-420000000000-22000000000000000−232323−23000000000000000000000000000000
χ654-44-44-2-44-424-22-444-4-4-22-22-424-2-4-4-2-22244002-2-2-222000000000000000000000000000000000000000000000
χ664-44-44-2-44-424-22-4-4-444-22-22-424-24422-2-2-4-4002-222-2-2000000000000000000000000000000000000000000000
χ674-44-4-244-42-4-24-420000-22-22-242-40000000000-220000000000000000000i6i6−i6−i6−i6−i6i6i60000000000000000000000
χ684-44-4-244-42-4-24-420000-22-22-242-40000000000-220000000000000000000−i6−i6i6i6i6i6−i6−i60000000000000000000000
χ694-44-4-24-442-4-24-42-4-444-22-222-4-24-2-2-4-44422002-222-2-2000000000000000000000000000000000000000000000
χ704-44-4-2-2-4422-2-22244-4-41-11-122-2-222-2-222-2-200-1111-1-10000000000000000000000000023−23−33−330000000000000
χ714-44-4-2-2-4422-2-22244-4-41-11-122-2-222-2-222-2-200-1111-1-100000000000000000000000000−23233−33−30000000000000
χ724-44-4-2-2-4422-2-222-4-4441-11-122-2-2-2-222-2-22200-11-1-11100000000000000000000000000003i−3i−3i3i0000000000000
χ734-44-4-2-2-4422-2-222-4-4441-11-122-2-2-2-222-2-22200-11-1-1110000000000000000000000000000−3i3i3i−3i0000000000000
χ744-4-444-200-42-42-2422−2222−22-222-2000022−22−22−2222−224-400−22−220-2222−22000000−2−222000000000000000000000000000000
χ754-4-444-200-42-42-2422−2222−22-222-2000022−22−22−2222−22-4400−22−2202-2−222200000022−2−2000000000000000000000000000000
χ764-4-444-200-42-42-24−2222−2222-222-20000−22222−22−2−22224-4002−22−20-22−222200000022−2−2000000000000000000000000000000
χ774-4-444-200-42-42-24−2222−2222-222-20000−22222−22−2−2222-44002−22−202-222−22000000−2−222000000000000000000000000000000
χ784-4-44-24002-42-44-222−2222−22-222-20000−2222−2222−22−220000−22−220000000−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ430000ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430000000000000000000000
χ794-4-44-24002-42-44-222−2222−22-222-20000−2222−2222−22−220000−22−2200000002ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ430000−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000000000000000000000
χ804-4-44-24002-42-44-2−2222−2222-222-200002−2−2222−22222−200002−22−200000002ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ470000−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000000000000000000000
χ814-4-44-24002-42-44-2−2222−2222-222-200002−2−2222−22222−200002−22−20000000−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ470000ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000000000000000000000
χ828888-4-4-8-8-4-4-4-4-4-40000222244440000000000-2-20000000000000000000000000000000000000000000000000
χ8388-8-8-4-400-4-4444442−42−424222-2-2000022−22−222222−22−222200002−2−22000000000000000000000000000000000000000000000
χ8488-8-8-4-400-4-44444−424242−4222-2-20000−222222−22−222222−220000−222−2000000000000000000000000000000000000000000000
χ858-88-8-4-48-844-4-44400002-22-2-4-44400000000002-20000000000000000000000000000000000000000000000000
χ868-8-88-4-4004444-4-442−4242−422-2-220000−2222−2222−2222−222200002−22−2000000000000000000000000000000000000000000000
χ878-8-88-4-4004444-4-4−4242−42422-2-22000022−2222−2222−2222−220000−22−22000000000000000000000000000000000000000000000

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