Finite Group Databasebeta

← Group #11773900

Character table — Group #11773900

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222222222244444444444444444466668888888888888888888888121212121212121212121212121224242424242424242424242424242424363636367272
order1222223344446666661212121236666666121212121212121212124444668812122424242424242424242424242424242444444412121212121212128888121212122424242424242424224488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111111111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1
χ911111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111i−i-1-1ii−i−iiiiiii−i−i−i−i−i−i11-1-1-1-11111-1-1-1-1i−ii−i-1-111ii−i−iii−i−i-1-111i−i
χ1011111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111i−i-1-1ii−i−iiiiiii−i−i−i−i−i−i-1-111-1-11111-1-1-1-1i−i−ii11-1-1ii−i−i−i−iii11-1-1−ii
χ1111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111−ii-1-1−i−iii−i−i−i−i−i−iiiiiii11-1-1-1-11111-1-1-1-1−ii−ii-1-111−i−iii−i−iii-1-111−ii
χ1211111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111−ii-1-1−i−iii−i−i−i−i−i−iiiiiii-1-111-1-11111-1-1-1-1−iii−i11-1-1−i−iiiii−i−i11-1-1i−i
χ1311111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111i−i-1-1ii−i−iiiiiii−i−i−i−i−i−i11-1-111-1-1-1-11111−iii−i-1-111−i−iiiii−i−i11-1-1−ii
χ1411111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111i−i-1-1ii−i−iiiiiii−i−i−i−i−i−i-1-11111-1-1-1-11111−ii−ii11-1-1−i−iii−i−iii-1-111i−i
χ1511111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111−ii-1-1−i−iii−i−i−i−i−i−iiiiiii11-1-111-1-1-1-11111i−i−ii-1-111ii−i−i−i−iii11-1-1i−i
χ1611111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111−ii-1-1−i−iii−i−i−i−i−i−iiiiiii-1-11111-1-1-1-11111i−ii−i11-1-1ii−i−iii−i−i-1-111−ii
χ172222222-122222-12-1-12-1-1-1-1-122-1-1-1-1-1-1-122-1-1-1-1222222-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1000022-1-1-1-1-1-1-1-122000000-1-1-1-10000000000
χ182222222-122222-12-1-12-1-1-1-1-122-1-1-1-1-1-1-122-1-1-1-1222222-1-1-2-2-1-11111-2-21111-2-21111000022-1-1-1-1-1-1-1-1-2-200000011110000000000
χ192222222-122222-12-1-12-1-1-1-1-122-1-1-1-1-1-1-122-1-1-1-122-2-2-2-2-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-10000-2-211111111-2-200000011110000000000
χ202222222-122222-12-1-12-1-1-1-1-122-1-1-1-1-1-1-122-1-1-1-122-2-2-2-2-1-1-2-2-1-11111-2-21111-2-211110000-2-21111111122000000-1-1-1-10000000000
χ212222222-1-2-2-2-22-12-1-121111-122-1-1-1-1-111-2-21111-2-22222-1-12i−2i11−i−iii2i2i−i−i−i−i−2i−2iiiii0000-2-2-1-1-1-111112i−2i000000−i−iii0000000000
χ222222222-1-2-2-2-22-12-1-121111-122-1-1-1-1-111-2-21111-2-22222-1-1−2i2i11ii−i−i−2i−2iiiii2i2i−i−i−i−i0000-2-2-1-1-1-11111−2i2i000000ii−i−i0000000000
χ232222222-1-2-2-2-22-12-1-121111-122-1-1-1-1-111-2-21111-2-2-2-2-2-2-1-12i−2i11−i−iii2i2i−i−i−i−i−2i−2iiiii0000221111-1-1-1-1−2i2i000000ii−i−i0000000000
χ242222222-1-2-2-2-22-12-1-121111-122-1-1-1-1-111-2-21111-2-2-2-2-2-2-1-1−2i2i11ii−i−i−2i−2iiiii2i2i−i−i−i−i0000221111-1-1-1-12i−2i000000−i−iii0000000000
χ25222222-122222-12-122-12222-1-1-122-1-1-122-1-1-1-1-1-1-1-10000-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1222200000000000022-1-1-1-10000-1-1-1-1000000
χ26222222-122222-12-122-12222-1-1-122-1-1-122-1-1-1-1-1-1-1-10000-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000000000000-2-2111100001111000000
χ27222222-122222-12-122-12222-1-1-122-1-1-122-1-1-1-1-1-1-1-10000-1-1-2-2-1-1-2-2-2-21111111111112222000000000000-2-2-1-1-1-100001111000000
χ28222222-122222-12-122-12222-1-1-122-1-1-122-1-1-1-1-1-1-1-10000-1-1-2-2-1-1-2-2-2-2111111111111-2-2-2-20000000000002211110000-1-1-1-1000000
χ29222222-12-2-2-2-2-12-122-1-2-2-2-2-1-1-122-1-1-1-2-2111111110000-1-12i−2i112i2i−2i−2i−i−i−i−i−i−iiiiiii22-2-20000000000002i−2i11-1-10000−i−iii000000
χ30222222-12-2-2-2-2-12-122-1-2-2-2-2-1-1-122-1-1-1-2-2111111110000-1-12i−2i112i2i−2i−2i−i−i−i−i−i−iiiiiii-2-222000000000000−2i2i-1-1110000ii−i−i000000
χ31222222-12-2-2-2-2-12-122-1-2-2-2-2-1-1-122-1-1-1-2-2111111110000-1-1−2i2i11−2i−2i2i2iiiiiii−i−i−i−i−i−i22-2-2000000000000−2i2i11-1-10000ii−i−i000000
χ32222222-12-2-2-2-2-12-122-1-2-2-2-2-1-1-122-1-1-1-2-2111111110000-1-1−2i2i11−2i−2i2i2iiiiiii−i−i−i−i−i−i-2-2220000000000002i−2i-1-1110000−i−iii000000
χ332222-2-22222-2-222222222222-2-2-2-2222-2-2222222-2-222-2-2-2-200-2-2000000000000000000002-222-2-222-2-20000000000000000000000
χ342222-2-22222-2-222222222222-2-2-2-2222-2-2222222-2-2-2-222-2-200-2-200000000000000000000-22-2-222-2-2220000000000000000000000
χ352222-2-222-2-222222222-2-2-2-22-2-2-2-222222-2-2-2-2-2-22222-2-2-2-2002200000000000000000000-2222-2-2-2-2220000000000000000000000
χ362222-2-222-2-222222222-2-2-2-22-2-2-2-222222-2-2-2-2-2-222-2-222-2-20022000000000000000000002-2-2-22222-2-20000000000000000000000
χ372222-2-22-122-2-22-12-1-12-1-1-1-1-1-2-211-1-1-11122-1-1-1-1-2-222-2-2110011−i3i3−i3i300−i3−i3i3i300−i3−i3i3i300002-2-1-111-1-11100000000−i3i3−i3i30000000000
χ382222-2-22-122-2-22-12-1-12-1-1-1-1-1-2-211-1-1-11122-1-1-1-1-2-222-2-2110011i3−i3i3−i300i3i3−i3−i300i3i3−i3−i300002-2-1-111-1-11100000000i3−i3i3−i30000000000
χ392222-2-22-122-2-22-12-1-12-1-1-1-1-1-2-211-1-1-11122-1-1-1-1-2-2-2-222110011−i3i3−i3i300−i3−i3i3i300−i3−i3i3i30000-2211-1-111-1-100000000i3−i3i3−i30000000000
χ402222-2-22-122-2-22-12-1-12-1-1-1-1-1-2-211-1-1-11122-1-1-1-1-2-2-2-222110011i3−i3i3−i300i3i3−i3−i300i3i3−i3−i30000-2211-1-111-1-100000000−i3i3−i3i30000000000
χ412222-2-22-1-2-2222-12-1-121111-1-2-211-1-1-1-1-1-2-211112222-2-21100-1-13−3−330033−3−300−3−3330000-22-1-11111-1-1000000003−3−330000000000
χ422222-2-22-1-2-2222-12-1-121111-1-2-211-1-1-1-1-1-2-211112222-2-21100-1-1−333−300−3−3330033−3−30000-22-1-11111-1-100000000−333−30000000000
χ432222-2-22-1-2-2222-12-1-121111-1-2-211-1-1-1-1-1-2-2111122-2-2221100-1-13−3−330033−3−300−3−33300002-211-1-1-1-11100000000−333−30000000000
χ442222-2-22-1-2-2222-12-1-121111-1-2-211-1-1-1-1-1-2-2111122-2-2221100-1-1−333−300−3−3330033−3−300002-211-1-1-1-111000000003−3−330000000000
χ452-22-22-2222i−2i2i−2i-2-222-2-22i2i−2i−2i22-22-22-2-22i−2i2i−2i2i2i−2i−2i2i−2i00002-2002i−2i00000000000000000000000000000000000000000000002-22i−2i00
χ462-22-22-2222i−2i2i−2i-2-222-2-22i2i−2i−2i22-22-22-2-22i−2i2i−2i2i2i−2i−2i2i−2i00002-2002i−2i0000000000000000000000000000000000000000000000-22−2i2i00
χ472-22-22-222−2i2i−2i2i-2-222-2-2−2i−2i2i2i22-22-22-2-2−2i2i−2i2i−2i−2i2i2i−2i2i00002-200−2i2i00000000000000000000000000000000000000000000002-2−2i2i00
χ482-22-22-222−2i2i−2i2i-2-222-2-2−2i−2i2i2i22-22-22-2-2−2i2i−2i2i−2i−2i2i2i−2i2i00002-200−2i2i0000000000000000000000000000000000000000000000-222i−2i00
χ492-22-2-22222i−2i−2i2i-2-222-2-22i2i−2i−2i2-22-222-2-2−2i2i2i−2i2i2i−2i−2i−2i2i0000-2200−2i2i00000000000000002i−2i2-2000000000000002-22i−2i00000000000000
χ502-22-2-22222i−2i−2i2i-2-222-2-22i2i−2i−2i2-22-222-2-2−2i2i2i−2i2i2i−2i−2i−2i2i0000-2200−2i2i0000000000000000−2i2i-2200000000000000-22−2i2i00000000000000
χ512-22-2-2222−2i2i2i−2i-2-222-2-2−2i−2i2i2i2-22-222-2-22i−2i−2i2i−2i−2i2i2i2i−2i0000-22002i−2i00000000000000002i−2i-2200000000000000-222i−2i00000000000000
χ522-22-2-2222−2i2i2i−2i-2-222-2-2−2i−2i2i2i2-22-222-2-22i−2i−2i2i−2i−2i2i2i2i−2i0000-22002i−2i0000000000000000−2i2i2-2000000000000002-2−2i2i00000000000000
χ532-22-2-22-122i−2i−2i2i1-2-12-212i2i−2i−2i-11-1-22-111−2i2i−ii−i−iiii−i00001-100i−i0000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ132i−2i2-200000000000000-11−ii0000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000
χ542-22-2-22-122i−2i−2i2i1-2-12-212i2i−2i−2i-11-1-22-111−2i2i−ii−i−iiii−i00001-100i−i0000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−2i2i-22000000000000001-1i−i0000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000
χ552-22-2-22-122i−2i−2i2i1-2-12-212i2i−2i−2i-11-1-22-111−2i2i−ii−i−iiii−i00001-100i−i0000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ132i−2i2-200000000000000-11−ii0000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000
χ562-22-2-22-122i−2i−2i2i1-2-12-212i2i−2i−2i-11-1-22-111−2i2i−ii−i−iiii−i00001-100i−i0000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−2i2i-22000000000000001-1i−i0000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000
χ572-22-2-22-12−2i2i2i−2i1-2-12-21−2i−2i2i2i-11-1-22-1112i−2ii−iii−i−i−ii00001-100−ii0000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ232i−2i-22000000000000001-1−ii0000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000
χ582-22-2-22-12−2i2i2i−2i1-2-12-21−2i−2i2i2i-11-1-22-1112i−2ii−iii−i−i−ii00001-100−ii0000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−2i2i2-200000000000000-11i−i0000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000
χ592-22-2-22-12−2i2i2i−2i1-2-12-21−2i−2i2i2i-11-1-22-1112i−2ii−iii−i−i−ii00001-100−ii0000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ232i−2i-22000000000000001-1−ii0000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000
χ602-22-2-22-12−2i2i2i−2i1-2-12-21−2i−2i2i2i-11-1-22-1112i−2ii−iii−i−i−ii00001-100−ii0000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−2i2i2-200000000000000-11i−i0000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000
χ61444444-2-24444-2-2-2-2-2-2-2-2-2-21-2-2-2-2111-2-2-2-21111-2-20000114411-2-2-2-2-2-21111-2-21111000000000000000000000000000000000000
χ62444444-2-24444-2-2-2-2-2-2-2-2-2-21-2-2-2-2111-2-2-2-21111-2-2000011-4-411222222-1-1-1-122-1-1-1-1000000000000000000000000000000000000
χ63444444-2-2-4-4-4-4-2-2-2-2-2-222221-2-2-2-21112222-1-1-1-1220000114i−4i-1-1−2i−2i2i2i−2i−2iiiii2i2i−i−i−i−i000000000000000000000000000000000000
χ64444444-2-2-4-4-4-4-2-2-2-2-2-222221-2-2-2-21112222-1-1-1-122000011−4i4i-1-12i2i−2i−2i2i2i−i−i−i−i−2i−2iiiii000000000000000000000000000000000000
χ654444-4-4-2444-4-4-24-244-24444-222-4-4-2-2-2-4-4-2-2-2-2-2-22200002200220000000000000000000000000000000000000000000000000000
χ664444-4-4-24-4-444-24-244-2-4-4-4-4-222-4-4-2-2-244222222-2-200002200-2-20000000000000000000000000000000000000000000000000000
χ674444-4-4-2-244-4-4-2-2-2-2-2-2-2-2-2-21222211122-2-21111220000-1-100-1-1−2i32i3−2i32i300i3i3−i3−i300i3i3−i3−i3000000000000000000000000000000000000
χ684444-4-4-2-244-4-4-2-2-2-2-2-2-2-2-2-21222211122-2-21111220000-1-100-1-12i3−2i32i3−2i300−i3−i3i3i300−i3−i3i3i3000000000000000000000000000000000000
χ694444-4-4-2-2-4-444-2-2-2-2-2-2222212222111-2-222-1-1-1-1-2-20000-1-1001123−23−232300−3−3330033−3−3000000000000000000000000000000000000
χ704444-4-4-2-2-4-444-2-2-2-2-2-2222212222111-2-222-1-1-1-1-2-20000-1-10011−232323−230033−3−300−3−333000000000000000000000000000000000000
χ7144-4-400440000-44-4-4-44000040000-4-440000000000004i−4i0000000000000000000000000000004i−4i00000000000000000000000000
χ7244-4-400440000-44-4-4-44000040000-4-44000000000000−4i4i000000000000000000000000000000−4i4i00000000000000000000000000
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χ7444-4-4004-20000-4-2-4224−2i32i3−2i32i3-2000022-20000−2i32i3−2i32i30000−4i4i0000000000000000000000000000002i−2i00−23230000000000000000000000
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χ784-44-44-44-2−4i4i−4i4i-424-22-42i2i−2i−2i-24-4-22-2222i−2i−4i4i2i2i−2i−2i−4i4i0000-22002i−2i0000000000000000000000000000000000000000000000000000
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χ824-44-44-4-2-24i−4i4i−4i22-2-222−2i−2i2i2i1-22-221-1-1−2i2i−2i2iii−i−i−2i2i00001-100i−i000000−3ζ7−3ζ233ζ7+3ζ233ζ7+3ζ23−3ζ7−3ζ2300−3ζ5−3ζ133ζ5+3ζ133ζ5+3ζ13−3ζ5−3ζ13000000000000000000000000000000000000
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χ904-44-4-44-2-2−4i4i4i−4i22-2-2222i2i−2i−2i12-22-21-1-1−2i2i2i−2i−i−iii−2i2i0000-1100i−i0000−2ζ5+2ζ132ζ5−2ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ132ζ7−2ζ23−2ζ7+2ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000000
χ914-4-44004400004-4-4-44-4000040000-44-400000000004i−4i0000000000000000000000000000004i−4i0000000000000000000000000000
χ924-4-44004400004-4-4-44-4000040000-44-40000000000−4i4i000000000000000000000000000000−4i4i0000000000000000000000000000
χ934-4-44004-2000042-42-2-423−23−2323-200002-22000023−23−2323004i−4i000000000000000000000000000000−2i2i00−2i32i3000000000000000000000000
χ944-4-44004-2000042-42-2-423−23−2323-200002-22000023−23−232300−4i4i0000000000000000000000000000002i−2i002i3−2i3000000000000000000000000
χ954-4-44004-2000042-42-2-4−232323−23-200002-220000−232323−23004i−4i000000000000000000000000000000−2i2i002i3−2i3000000000000000000000000
χ964-4-44004-2000042-42-2-4−232323−23-200002-220000−232323−2300−4i4i0000000000000000000000000000002i−2i00−2i32i3000000000000000000000000
χ9788-8-800-480000484-8-8-40000-4000044-4000000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-800-4-400004-4444-4−4i34i3−4i34i320000-2-2200002i3−2i32i3−2i30000000000000000000000000000000000000000000000000000000000000000
χ9988-8-800-4-400004-4444-44i3−4i34i3−4i320000-2-220000−2i32i3−2i32i30000000000000000000000000000000000000000000000000000000000000000
χ1008-8-8800-480000-4-84-8840000-400004-44000000000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-8800-4-40000-4444-4443−43−434320000-22-20000−232323−230000000000000000000000000000000000000000000000000000000000000000
χ1028-8-8800-4-40000-4444-44−434343−4320000-22-2000023−23−23230000000000000000000000000000000000000000000000000000000000000000

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