Finite Group Databasebeta

← Group #11784944

Character table — Group #11784944

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222222222222444444444444444444448888888888888888888888121212121212121224242424242424242424242424242424242424243636363636363636
order12442223344466121212123666666666121212121212121212124466121212121212121212121212121212121212222244444466668812121212121212122424242422448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1
χ911-1-11-1-11111-111-1-1-1-1111-1-1-11-1-1-11111-1-111-1-1i−i1-11-1iiiiiiii−i−i−i−i−i−i−i−i111-1-1-11-1i−i111-1i−i-1-11-1ii−i−iii−i−i1-11-1ii−i−i
χ1011-1-11-1-11111-111-1-1-1-1111-1-1-11-1-1-11111-1-111-1-1i−i1-11-1iiiiiiii−i−i−i−i−i−i−i−i11-11-1-1-11i−i11-11−ii-1-1-11ii−i−i−i−iii-11-11−i−iii
χ1111-1-11-1-11111-111-1-1-1-1111-1-1-11-1-1-11111-1-111-1-1i−i1-11-1iiiiiiii−i−i−i−i−i−i−i−i-1-11-1111-1−ii-1-11-1i−i111-1−i−iiiii−i−i-11-11−i−iii
χ1211-1-11-1-11111-111-1-1-1-1111-1-1-11-1-1-11111-1-111-1-1i−i1-11-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1111-11−ii-1-1-11−ii11-11−i−iii−i−iii1-11-1ii−i−i
χ1311-1-11-1-11111-111-1-1-1-1111-1-1-11-1-1-11111-1-111-1-1−ii1-11-1−i−i−i−i−i−i−i−iiiiiiiii111-1-1-11-1−ii111-1−ii-1-11-1−i−iii−i−iii1-11-1−i−iii
χ1411-1-11-1-11111-111-1-1-1-1111-1-1-11-1-1-11111-1-111-1-1−ii1-11-1−i−i−i−i−i−i−i−iiiiiiiii11-11-1-1-11−ii11-11i−i-1-1-11−i−iiiii−i−i-11-11ii−i−i
χ1511-1-11-1-11111-111-1-1-1-1111-1-1-11-1-1-11111-1-111-1-1−ii1-11-1−i−i−i−i−i−i−i−iiiiiiiii-1-11-1111-1i−i-1-11-1−ii111-1ii−i−i−i−iii-11-11ii−i−i
χ1611-1-11-1-11111-111-1-1-1-1111-1-1-11-1-1-11111-1-111-1-1−ii1-11-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1111-11i−i-1-1-11i−i11-11ii−i−iii−i−i1-11-1−i−iii
χ1722222222-12222-122-1-1-12-1-12-1-1-1-1222-1-12-1-1-1-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1002200220000-1-12200-1-10000-1-1-1-100000000
χ1822222222-12222-122-1-1-12-1-12-1-1-1-1222-1-12-1-1-1-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100-2-200-2-2000011-2-200110000111100000000
χ1922222222-12222-122-1-1-12-1-12-1-1-1-1222-1-12-1-1-1-1-1-2-2-1-1-1-1-2-2111111-2-2111111002200220000-1-1-2-200-1-10000111100000000
χ2022222222-12222-122-1-1-12-1-12-1-1-1-1222-1-12-1-1-1-1-1-2-2-1-1-1-1-2-2111111-2-211111100-2-200-2-20000112200110000-1-1-1-100000000
χ212222222-12222-12-1-122-1-122-12-1-1-1-1-1-122-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-12200220022-1-10000-1-100-1-1-1-1000000000000
χ222222222-12222-12-1-122-1-122-12-1-1-1-1-1-122-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-2-200-2-200-2-211000011001111000000000000
χ232222222-12222-12-1-122-1-122-12-1-1-1-1-1-122-12-1-1-1-1-2-2-1-1-1-111-2-2111111-2-2111122002200-2-2-1-10000-1-1001111000000000000
χ242222222-12222-12-1-122-1-122-12-1-1-1-1-1-122-12-1-1-1-1-2-2-1-1-1-111-2-2111111-2-21111-2-200-2-200221100001100-1-1-1-1000000000000
χ2522222-2-222-2-22222222222-2-2-22-2-2-2-2-2-2-222-2-222002-2-2200000000000000002-2002-200002-200002-2000000000000000000
χ2622222-2-222-2-22222222222-2-2-22-2-2-2-2-2-2-222-2-222002-2-220000000000000000-2200-220000-220000-22000000000000000000
χ2722222-2-2-12-2-22-12-1-122-1-12-21-2-111111-2-2-1211-1-100-111-13−30033−3−33−30033−3−32-2002-20000-110000-11003−33−3000000000000
χ2822222-2-2-12-2-22-12-1-122-1-12-21-2-111111-2-2-1211-1-100-111-13−30033−3−33−30033−3−3-2200-2200001-100001-100−33−33000000000000
χ2922222-2-2-12-2-22-12-1-122-1-12-21-2-111111-2-2-1211-1-100-111-1−3300−3−333−3300−3−3332-2002-20000-110000-1100−33−33000000000000
χ3022222-2-2-12-2-22-12-1-122-1-12-21-2-111111-2-2-1211-1-100-111-1−3300−3−333−3300−3−333-2200-2200001-100001-1003−33−3000000000000
χ312222-22-2222-2-22222222-2-2-222222-22-22-2-2-2222200-2-2-2-20000000000000000002-200-2200002-20000-220000000000000000
χ322222-22-2222-2-22222222-2-2-222222-22-22-2-2-2222200-2-2-2-2000000000000000000-22002-20000-2200002-20000000000000000
χ332222-22-22-12-2-22-122-1-1-1-2112-1-1-1-1-22-2-11-21-1-1-1-100111100−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3002-200-220000-1100001-10000−i3i3−i3i300000000
χ342222-22-22-12-2-22-122-1-1-1-2112-1-1-1-1-22-2-11-21-1-1-1-100111100−i3i3−i3i3−i3i300−i3i3−i3i3−i3i300-22002-200001-10000-110000i3−i3i3−i300000000
χ352222-22-22-12-2-22-122-1-1-1-2112-1-1-1-1-22-2-11-21-1-1-1-100111100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3002-200-220000-1100001-10000i3−i3i3−i300000000
χ362222-22-22-12-2-22-122-1-1-1-2112-1-1-1-1-22-2-11-21-1-1-1-100111100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i300-22002-200001-10000-110000−i3i3−i3i300000000
χ372222-2-2222-22-22222222-2-22-2-22-2-22-22-22-2-2-2-22200-222-2000000000000000000000000000000000000000000002-2-220000
χ382222-2-2222-22-22222222-2-22-2-22-2-22-22-22-2-2-2-22200-222-200000000000000000000000000000000000000000000-222-20000
χ3922-2-222222-2-2-222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-20022-2-200000000000000002-200-2200002-20000-22000000000000000000
χ4022-2-222222-2-2-222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-20022-2-20000000000000000-22002-20000-2200002-2000000000000000000
χ4122-2-2222-12-2-2-2-1211-2-2-1-122-12-1-1-1-111-2-21-2111100-1-111−i3i300−i3−i3i3i3i3−i300i3i3−i3−i32-200-220000-1100001-100−i3i3i3−i3000000000000
χ4222-2-2222-12-2-2-2-1211-2-2-1-122-12-1-1-1-111-2-21-2111100-1-111−i3i300−i3−i3i3i3i3−i300i3i3−i3−i3-22002-200001-10000-1100i3−i3−i3i3000000000000
χ4322-2-2222-12-2-2-2-1211-2-2-1-122-12-1-1-1-111-2-21-2111100-1-111i3−i300i3i3−i3−i3−i3i300−i3−i3i3i32-200-220000-1100001-100i3−i3−i3i3000000000000
χ4422-2-2222-12-2-2-2-1211-2-2-1-122-12-1-1-1-111-2-21-2111100-1-111i3−i300i3i3−i3−i3−i3i300−i3−i3i3i3-22002-200001-10000-1100−i3i3i3−i3000000000000
χ4522-2-22-2-22-122-22-1-2-211-12-11-21-111-222-1-1-21-1-1112i−2i-11-112i2i−i−i−i−i−i−i−2i−2iiiiiii002-2002-20000-112i−2i00-110000−i−iii00000000
χ4622-2-22-2-22-122-22-1-2-211-12-11-21-111-222-1-1-21-1-1112i−2i-11-112i2i−i−i−i−i−i−i−2i−2iiiiiii00-2200-2200001-1−2i2i001-10000ii−i−i00000000
χ4722-2-22-2-22-122-22-1-2-211-12-11-21-111-222-1-1-21-1-111−2i2i-11-11−2i−2iiiiiii2i2i−i−i−i−i−i−i002-2002-20000-11−2i2i00-110000ii−i−i00000000
χ4822-2-22-2-22-122-22-1-2-211-12-11-21-111-222-1-1-21-1-111−2i2i-11-11−2i−2iiiiiii2i2i−i−i−i−i−i−i00-2200-2200001-12i−2i001-10000−i−iii00000000
χ4922-2-22-2-2-1222-2-1211-2-2-1-12-21-2-1111-1-1221-2-1-1112i−2i-11-11−i−i2i2i−i−i−i−iii−2i−2iiiii2200-2-2002i−2i-1-100001100−i−iii000000000000
χ5022-2-22-2-2-1222-2-1211-2-2-1-12-21-2-1111-1-1221-2-1-1112i−2i-11-11−i−i2i2i−i−i−i−iii−2i−2iiiii-2-2002200−2i2i110000-1-100ii−i−i000000000000
χ5122-2-22-2-2-1222-2-1211-2-2-1-12-21-2-1111-1-1221-2-1-111−2i2i-11-11ii−2i−2iiiii−i−i2i2i−i−i−i−i2200-2-200−2i2i-1-100001100ii−i−i000000000000
χ5222-2-22-2-2-1222-2-1211-2-2-1-12-21-2-1111-1-1221-2-1-111−2i2i-11-11ii−2i−2iiiii−i−i2i2i−i−i−i−i-2-20022002i−2i110000-1-100−i−iii000000000000
χ5322-2-2-22-222-22222-2-2-2-22-2-2-222222-2-22-2222-2-2-2-200-2-2220000000000000000000000000000000000000000000022-2-20000
χ5422-2-2-22-222-22222-2-2-2-22-2-2-222222-2-22-2222-2-2-2-200-2-22200000000000000000000000000000000000000000000-2-2220000
χ5522-2-2-2-22222-2222-2-2-2-22-2-22-2-22-2-222-22-22222-2-200-22-220000000000000000002200-2-20000220000-2-20000000000000000
χ5622-2-2-2-22222-2222-2-2-2-22-2-22-2-22-2-222-22-22222-2-200-22-22000000000000000000-2-200220000-2-20000220000000000000000
χ5722-2-2-2-222-12-222-1-2-211-1-21-1-21-11122-2-112-1-1-111001-11-1003−33−33−300−33−33−33002200-2-20000-1-100001100003−3−3300000000
χ5822-2-2-2-222-12-222-1-2-211-1-21-1-21-11122-2-112-1-1-111001-11-1003−33−33−300−33−33−3300-2-200220000110000-1-10000−333−300000000
χ5922-2-2-2-222-12-222-1-2-211-1-21-1-21-11122-2-112-1-1-111001-11-100−33−33−33003−33−33−3002200-2-20000-1-10000110000−333−300000000
χ6022-2-2-2-222-12-222-1-2-211-1-21-1-21-11122-2-112-1-1-111001-11-100−33−33−33003−33−33−300-2-200220000110000-1-100003−3−3300000000
χ614444444-2-2444-2-2-2-2-2-21-2-2-2-2-2111-2-2-2-2-2-2-21111441111-2-2-2-21111-2-2-2-21111000000000000000000000000000000000000
χ624444444-2-2444-2-2-2-2-2-21-2-2-2-2-2111-2-2-2-2-2-2-21111-4-411112222-1-1-1-12222-1-1-1-1000000000000000000000000000000000000
χ6344444-4-44-2-4-444-244-2-2-24-22-42-222-4-4-4224-222-2-200-222-20000000000000000000000000000000000000000000000000000
χ6444444-4-4-2-2-4-44-2-2-2-2-2-21-2-22221-1-122222-2-2-1-111001-1-1123−2300−3−33323−2300−3−333000000000000000000000000000000000000
χ6544444-4-4-2-2-4-44-2-2-2-2-2-21-2-22221-1-122222-2-2-1-111001-1-11−23230033−3−3−23230033−3−3000000000000000000000000000000000000
χ664444-44-4-244-4-4-24-2-244-22-4-4-24-2-2-22-224-42-4-2-2-2-20022220000000000000000000000000000000000000000000000000000
χ674444-44-4-2-24-4-4-2-2-2-2-2-21222-2-21112-22-2222111100-1-1-1-100−2i32i3i3−i3i3−i300−2i32i3i3−i3i3−i3000000000000000000000000000000000000
χ684444-44-4-2-24-4-4-2-2-2-2-2-21222-2-21112-22-2222111100-1-1-1-1002i3−2i3−i3i3−i3i3002i3−2i3−i3i3−i3i3000000000000000000000000000000000000
χ694444-4-444-2-44-44-244-2-2-2-42-2-42-2224-442-2-4222-2-2002-2-220000000000000000000000000000000000000000000000000000
χ704444-4-44-24-44-4-24-2-244-22-442-4-222-22-2-442-422-2-2002-2-220000000000000000000000000000000000000000000000000000
χ714444-4-44-2-2-44-4-2-2-2-2-2-2122-2221-1-1-22-22-222-1-11100-111-100003i−3i−3i3i00003i−3i−3i3i000000000000000000000000000000000000
χ724444-4-44-2-2-44-4-2-2-2-2-2-2122-2221-1-1-22-22-222-1-11100-111-10000−3i3i3i−3i0000−3i3i3i−3i000000000000000000000000000000000000
χ7344-4-44444-2-4-4-44-2-4-422-24-2-24-2-2-2-24-4-422-42222200-2-2220000000000000000000000000000000000000000000000000000
χ7444-4-4444-2-2-4-4-4-2-222221-2-2-2-2-2111-2222222-1-1-1-10011-1-1−2i32i300i3i3−i3−i32i3−2i300−i3−i3i3i3000000000000000000000000000000000000
χ7544-4-4444-2-2-4-4-4-2-222221-2-2-2-2-2111-2222222-1-1-1-10011-1-12i3−2i300−i3−i3i3i3−2i32i300i3i3−i3−i3000000000000000000000000000000000000
χ7644-4-44-4-4-2-244-4-2-222221-2-22221-1-12-2-2-2-22211-1-14i−4i1-11-1−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i000000000000000000000000000000000000
χ7744-4-44-4-4-2-244-4-2-222221-2-22221-1-12-2-2-2-22211-1-1−4i4i1-11-12i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii000000000000000000000000000000000000
χ7844-4-4-44-44-2-4444-2-4-422-2-4224-2-2-2-2-4-442-24-222220022-2-20000000000000000000000000000000000000000000000000000
χ7944-4-4-44-4-24-444-2422-4-4-22-4-4-24-2-2-222-2-44-2422220022-2-20000000000000000000000000000000000000000000000000000
χ8044-4-4-44-4-2-2-444-2-222221222-2-211122-22-2-2-2-1-1-1-100-1-11100003-3-330000-333-3000000000000000000000000000000000000
χ8144-4-4-44-4-2-2-444-2-222221222-2-211122-22-2-2-2-1-1-1-100-1-1110000-333-300003-3-33000000000000000000000000000000000000
χ8244-4-4-4-44-244-44-2422-4-4-22-442-4-222-2-224-4-24-2-222002-22-20000000000000000000000000000000000000000000000000000
χ8344-4-4-4-44-2-24-44-2-22222122-2221-1-1-2-22-22-2-211-1-100-11-110023−23−33−3300−23233−33−3000000000000000000000000000000000000
χ8444-4-4-4-44-2-24-44-2-22222122-2221-1-1-2-22-22-2-211-1-100-11-1100−23233−33−30023−23−33−33000000000000000000000000000000000000
χ854-44i−4i00044000-4-44i−4i4i−4i400000-4000000000004i−4i0000000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13
χ864-44i−4i00044000-4-44i−4i4i−4i400000-4000000000004i−4i000000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13
χ874-4−4i4i00044000-4-4−4i4i−4i4i400000-400000000000−4i4i000000000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23
χ884-4−4i4i00044000-4-4−4i4i−4i4i400000-400000000000−4i4i0000000000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23
χ898-88i−8i0008-4000-848i−8i−4i4i-400000400000000000−4i4i0000000000000000000000000000000000000000000000000000000000
χ908-88i−8i000-480004-8−4i4i8i−8i-400000400000000000−4i4i0000000000000000000000000000000000000000000000000000000000
χ918-88i−8i000-4-400044−4i4i−4i4i200000-26-600000006i−6i2i−2i0000000000000000000000000000000000000000000000000000000000
χ928-88i−8i000-4-400044−4i4i−4i4i200000-2-660000000−6i6i2i−2i0000000000000000000000000000000000000000000000000000000000
χ938-8−8i8i0008-4000-84−8i8i4i−4i-4000004000000000004i−4i0000000000000000000000000000000000000000000000000000000000
χ948-8−8i8i000-480004-84i−4i−8i8i-4000004000000000004i−4i0000000000000000000000000000000000000000000000000000000000
χ958-8−8i8i000-4-4000444i−4i4i−4i200000-26-60000000−6i6i−2i2i0000000000000000000000000000000000000000000000000000000000
χ968-8−8i8i000-4-4000444i−4i4i−4i200000-2-6600000006i−6i−2i2i0000000000000000000000000000000000000000000000000000000000

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