Finite Group Databasebeta

← Group #11774007

Character table — Group #11774007

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222222222244444444444444444466668888888888888888888888121212121212121212121212121224242424242424242424242424242424363636367272
order1222223344446666661212121236666666121212121212121212122244668812122424242424242424242424242424242424666688881212121224668812122424242424242424888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ41111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111
χ51111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1
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
χ71111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ911111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111i−i-1-1ii−i−iiiiiii−i−i−i−i−i−i1-11111ii−i−i-1-1-1-11-111i−i-1-1ii−i−iii−i−iii−i−i-11
χ1011111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111i−i-1-1ii−i−iiiiiii−i−i−i−i−i−i1-11111−i−iii-1-1-1-1-11-1-1i−i11ii−i−i−i−iii−i−iii1-1
χ1111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111−ii-1-1−i−iii−i−i−i−i−i−iiiiiii1-11111ii−i−i-1-1-1-1-11-1-1−ii11−i−iiiii−i−iii−i−i1-1
χ1211111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111−ii-1-1−i−iii−i−i−i−i−i−iiiiiii1-11111−i−iii-1-1-1-11-111−ii-1-1−i−iii−i−iii−i−iii-11
χ1311111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111i−i-1-1ii−i−iiiiiii−i−i−i−i−i−i-11-1-1-1-1ii−i−i11111-111−ii-1-1−i−iiiii−i−i−i−iii1-1
χ1411111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111i−i-1-1ii−i−iiiiiii−i−i−i−i−i−i-11-1-1-1-1−i−iii1111-11-1-1−ii11−i−iii−i−iiiii−i−i-11
χ1511111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111−ii-1-1−i−iii−i−i−i−i−i−iiiiiii-11-1-1-1-1ii−i−i1111-11-1-1i−i11ii−i−iii−i−i−i−iii-11
χ1611111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111−ii-1-1−i−iii−i−i−i−i−i−iiiiiii-11-1-1-1-1−i−iii11111-111i−i-1-1ii−i−i−i−iiiii−i−i1-1
χ172222222-1222222-1-1-122222-122-1-1-1-1-122-1-1-1-1-1-1-1-10000-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000002222000022-1-100-1-10000-1-1-1-1000000
χ182222222-1222222-1-1-122222-122-1-1-1-1-122-1-1-1-1-1-1-1-10000-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000-2-2-2-20000-2-211001100001111000000
χ192222222-1222222-1-1-122222-122-1-1-1-1-122-1-1-1-1-1-1-1-10000-1-1-2-2-1-1-2-2-2-211111111111100000022220000-2-21100110000-1-1-1-1000000
χ202222222-1222222-1-1-122222-122-1-1-1-1-122-1-1-1-1-1-1-1-10000-1-1-2-2-1-1-2-2-2-2111111111111000000-2-2-2-2000022-1-100-1-100001111000000
χ212222222-1-2-2-2-222-1-1-12-2-2-2-2-122-1-1-1-1-1-2-2111111110000-1-12i−2i112i2i−2i−2i−i−i−i−i−i−iiiiiii0000002i2i−2i−2i00002-2-1-100110000−i−iii000000
χ222222222-1-2-2-2-222-1-1-12-2-2-2-2-122-1-1-1-1-1-2-2111111110000-1-12i−2i112i2i−2i−2i−i−i−i−i−i−iiiiiii000000−2i−2i2i2i0000-221100-1-10000ii−i−i000000
χ232222222-1-2-2-2-222-1-1-12-2-2-2-2-122-1-1-1-1-1-2-2111111110000-1-1−2i2i11−2i−2i2i2iiiiiii−i−i−i−i−i−i0000002i2i−2i−2i0000-221100-1-10000−i−iii000000
χ242222222-1-2-2-2-222-1-1-12-2-2-2-2-122-1-1-1-1-1-2-2111111110000-1-1−2i2i11−2i−2i2i2iiiiiii−i−i−i−i−i−i000000−2i−2i2i2i00002-2-1-100110000ii−i−i000000
χ25222222-122222-1-1222-1-1-1-1-1-1-1-122-1-1-1-1-122-1-1-1-1222222-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-10000-1-1-1-100002200-1-1-1-10000000000
χ26222222-122222-1-1222-1-1-1-1-1-1-1-122-1-1-1-1-122-1-1-1-1222222-1-1-2-2-1-11111-2-21111-2-2111122-1-1-1-10000-1-1-1-10000-2-20011110000000000
χ27222222-122222-1-1222-1-1-1-1-1-1-1-122-1-1-1-1-122-1-1-1-122-2-2-2-2-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-21111000011110000-2-20011110000000000
χ28222222-122222-1-1222-1-1-1-1-1-1-1-122-1-1-1-1-122-1-1-1-122-2-2-2-2-1-1-2-2-1-11111-2-21111-2-21111-2-211110000111100002200-1-1-1-10000000000
χ29222222-12-2-2-2-2-1-1222-11111-1-1-122-1-1-111-2-21111-2-222-2-2-1-12i−2i11−i−iii2i2i−i−i−i−i−2i−2iiiii2-2-1-1-1-10000111100002i−2i00−i−iii0000000000
χ30222222-12-2-2-2-2-1-1222-11111-1-1-122-1-1-111-2-21111-2-222-2-2-1-1−2i2i11ii−i−i−2i−2iiiii2i2i−i−i−i−i2-2-1-1-1-1000011110000−2i2i00ii−i−i0000000000
χ31222222-12-2-2-2-2-1-1222-11111-1-1-122-1-1-111-2-21111-2-2-2-222-1-12i−2i11−i−iii2i2i−i−i−i−i−2i−2iiiii-2211110000-1-1-1-10000−2i2i00ii−i−i0000000000
χ32222222-12-2-2-2-2-1-1222-11111-1-1-122-1-1-111-2-21111-2-2-2-222-1-1−2i2i11ii−i−i−2i−2iiiii2i2i−i−i−i−i-2211110000-1-1-1-100002i−2i00−i−iii0000000000
χ332222-2-22222-2-222222222222-2-2-2-2222-2-2222222-2-222-2-2-2-200-2-20000000000000000-2222-2-2000022-2-20000000000000000000000
χ342222-2-22222-2-222222222222-2-2-2-2222-2-2222222-2-2-2-222-2-200-2-200000000000000002-2-2-2220000-2-2220000000000000000000000
χ352222-2-222-2-222222222-2-2-2-22-2-2-2-222222-2-2-2-2-2-2222222-2-200220000000000000000-2-222-2-20000-2-2220000000000000000000000
χ362222-2-222-2-222222222-2-2-2-22-2-2-2-222222-2-2-2-2-2-222-2-2-2-2-2-20022000000000000000022-2-222000022-2-20000000000000000000000
χ372222-2-2-1222-2-2-1-1222-1-1-1-1-1-111-2-2-1-1-11122-1-1-1-1-2-222-2-2110011−i3i3−i3i300−i3−i3i3i300−i3−i3i3i3-22-1-1110000-1-11100000000−i3i3−i3i30000000000
χ382222-2-2-1222-2-2-1-1222-1-1-1-1-1-111-2-2-1-1-11122-1-1-1-1-2-222-2-2110011i3−i3i3−i300i3i3−i3−i300i3i3−i3−i3-22-1-1110000-1-11100000000i3−i3i3−i30000000000
χ392222-2-2-1222-2-2-1-1222-1-1-1-1-1-111-2-2-1-1-11122-1-1-1-1-2-2-2-222110011−i3i3−i3i300−i3−i3i3i300−i3−i3i3i32-211-1-1000011-1-100000000i3−i3i3−i30000000000
χ402222-2-2-1222-2-2-1-1222-1-1-1-1-1-111-2-2-1-1-11122-1-1-1-1-2-2-2-222110011i3−i3i3−i300i3i3−i3−i300i3i3−i3−i32-211-1-1000011-1-100000000−i3i3−i3i30000000000
χ412222-2-2-12-2-222-1-1222-11111-111-2-2-1-1-1-1-1-2-211112222221100-1-13−3−330033−3−300−3−333-2-2-1-111000011-1-1000000003−3−330000000000
χ422222-2-2-12-2-222-1-1222-11111-111-2-2-1-1-1-1-1-2-211112222221100-1-1−333−300−3−3330033−3−3-2-2-1-111000011-1-100000000−333−30000000000
χ432222-2-2-12-2-222-1-1222-11111-111-2-2-1-1-1-1-1-2-2111122-2-2-2-21100-1-13−3−330033−3−300−3−3332211-1-10000-1-11100000000−333−30000000000
χ442222-2-2-12-2-222-1-1222-11111-111-2-2-1-1-1-1-1-2-2111122-2-2-2-21100-1-1−333−300−3−3330033−3−32211-1-10000-1-111000000003−3−330000000000
χ452-22-22-2222i−2i2i−2i2-22-2-2-22i2i−2i−2i22-22-22-2-22i−2i2i−2i2i2i−2i−2i2i−2i00002-2002i−2i0000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ462-22-22-2222i−2i2i−2i2-22-2-2-22i2i−2i−2i22-22-22-2-22i−2i2i−2i2i2i−2i−2i2i−2i00002-2002i−2i00000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ472-22-22-222−2i2i−2i2i2-22-2-2-2−2i−2i2i2i22-22-22-2-2−2i2i−2i2i−2i−2i2i2i−2i2i00002-200−2i2i00000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ482-22-22-222−2i2i−2i2i2-22-2-2-2−2i−2i2i2i22-22-22-2-2−2i2i−2i2i−2i−2i2i2i−2i2i00002-200−2i2i0000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ492-22-2-22222i−2i−2i2i2-22-2-2-22i2i−2i−2i2-22-222-2-2−2i2i2i−2i2i2i−2i−2i−2i2i0000-2200−2i2i00000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000
χ502-22-2-22222i−2i−2i2i2-22-2-2-22i2i−2i−2i2-22-222-2-2−2i2i2i−2i2i2i−2i−2i−2i2i0000-2200−2i2i0000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000
χ512-22-2-2222−2i2i2i−2i2-22-2-2-2−2i−2i2i2i2-22-222-2-22i−2i−2i2i−2i−2i2i2i2i−2i0000-22002i−2i0000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000
χ522-22-2-2222−2i2i2i−2i2-22-2-2-2−2i−2i2i2i2-22-222-2-22i−2i−2i2i−2i−2i2i2i2i−2i0000-22002i−2i00000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000
χ532-22-2-222-12i−2i−2i2i2-2-111-22i2i−2i−2i-1-221-1-111−2i2i−ii−i−iiii−i00001-100i−i0000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000−i3i3003−30000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13000000
χ542-22-2-222-12i−2i−2i2i2-2-111-22i2i−2i−2i-1-221-1-111−2i2i−ii−i−iiii−i00001-100i−i0000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000i3−i300−330000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13000000
χ552-22-2-222-12i−2i−2i2i2-2-111-22i2i−2i−2i-1-221-1-111−2i2i−ii−i−iiii−i00001-100i−i0000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000i3−i300−330000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13000000
χ562-22-2-222-12i−2i−2i2i2-2-111-22i2i−2i−2i-1-221-1-111−2i2i−ii−i−iiii−i00001-100i−i0000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000−i3i3003−30000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13000000
χ572-22-2-222-1−2i2i2i−2i2-2-111-2−2i−2i2i2i-1-221-1-1112i−2ii−iii−i−i−ii00001-100−ii0000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000i3−i3003−30000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23000000
χ582-22-2-222-1−2i2i2i−2i2-2-111-2−2i−2i2i2i-1-221-1-1112i−2ii−iii−i−i−ii00001-100−ii0000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000−i3i300−330000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23000000
χ592-22-2-222-1−2i2i2i−2i2-2-111-2−2i−2i2i2i-1-221-1-1112i−2ii−iii−i−i−ii00001-100−ii0000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000−i3i300−330000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23000000
χ602-22-2-222-1−2i2i2i−2i2-2-111-2−2i−2i2i2i-1-221-1-1112i−2ii−iii−i−i−ii00001-100−ii0000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000i3−i3003−30000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23000000
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
χ654444-4-44-244-4-444-2-2-244444-2-4-422-2-2-2-4-4-2-2-2-2-2-22200002200220000000000000000000000000000000000000000000000000000
χ664444-4-44-2-4-44444-2-2-24-4-4-4-4-2-4-422-2-2-244222222-2-200002200-2-20000000000000000000000000000000000000000000000000000
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
χ7144-4-400440000-44-4-44-4000040000-44-40000000000004i−4i00000000000000000000000000000000004i−4i0000000000000000000000
χ7244-4-400440000-44-4-44-4000040000-44-4000000000000−4i4i0000000000000000000000000000000000−4i4i0000000000000000000000
χ7344-4-400-2400002-2-4-44223−2323−23-200002-22000023−2323−2300004i−4i00000000000000000000000000−2i32i3000000−2i2i0000000000000000000000
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χ1028-8-8800-4-40000444-44-44i3−4i3−4i34i320000-2-220000−2i32i32i3−2i30000000000000000000000000000000000000000000000000000000000000000

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