Finite Group Databasebeta

← Group #11782409

Character table — Group #11782409

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222244444444444444444888888888888888888888881212121212121212121212122424242424242424242424244848487272144
order1222334444666666121212123466612121212121212121212121288121212121224242424242424242424242424242424888824242424242424244488121212122424242441212884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ51111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-111-1
χ61111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11
χ71111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11
χ81111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111-1
χ92222222-22-222222222222-2222-2-2-2-2222222-2-200-2-2-2-2-200000000000000000000000000002-20022-2-20000000000
χ102222222-22-222222222222-2222-2-2-2-2222222-2-200-2-2-2-2-20000000000000000000000000000-2200-2-2220000000000
χ11222222-22-22222222-2-2-2-22-222222-2-2-2-2-2-2-2-22200-222-2-2000000000000000022-2-22222-2-2-2-2000000000000000000
χ12222222-22-22222222-2-2-2-22-222222-2-2-2-2-2-2-2-22200-222-2-20000000000000000-2-222-2-2-2-22222000000000000000000
χ13222222-2-2-2-2222222-2-2-2-222222-2-222-2-2-2-2-2-2-2-2002-2-22200000000000000000000000000000000000000000002i−2i0
χ14222222-2-2-2-2222222-2-2-2-222222-2-222-2-2-2-2-2-2-2-2002-2-2220000000000000000000000000000000000000000000−2i2i0
χ1522222-12222222-1-1-12222-12-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000002200-1-1-1-100002-1-1000
χ1622222-12222222-1-1-12222-12-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-20011110000-211000
χ1722222-12222222-1-1-12222-12-1-1-1-1-122-1-1-1-1-1-122-2-2-1-1-1-1-1-2-2-2-21111111111110000000000002200-1-1-1-10000-211000
χ1822222-12222222-1-1-12222-12-1-1-1-1-122-1-1-1-1-1-122-2-2-1-1-1-1-1-2-2-2-2111111111111000000000000-2-200111100002-1-1000
χ1922222-12-22-2222-1-1-12222-1-2-1-1-111-2-2-1-1-1-1-1-1-2-200111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i30000000000002-200-1-11100000−i3i3000
χ2022222-12-22-2222-1-1-12222-1-2-1-1-111-2-2-1-1-1-1-1-1-2-200111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3000000000000-220011-1-100000i3−i3000
χ2122222-12-22-2222-1-1-12222-1-2-1-1-111-2-2-1-1-1-1-1-1-2-200111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i30000000000002-200-1-11100000i3−i3000
χ2222222-12-22-2222-1-1-12222-1-2-1-1-111-2-2-1-1-1-1-1-1-2-200111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3000000000000-220011-1-100000−i3i3000
χ232222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-12-1-12-1-1-1-1222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-100220000-1-1-1-1000000
χ242222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-12-1-12-1-1-1-1222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-21111111100-2-200001111000000
χ252222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-12-1-12-1-1-1-1-2-22-1-1-1-11111-2-21111-2-211112222-1-1-1-1-1-1-1-100-2-200001111000000
χ262222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-12-1-12-1-1-1-1-2-22-1-1-1-11111-2-21111-2-21111-2-2-2-21111111100220000-1-1-1-1000000
χ272222-12-22-22-1-1-12221111-1-2-1-1-12211-211-211-1-100-2-1-11133−3−30033−3−30033−3−322-2-2-1-1-1-111110000000033−3−3000000
χ282222-12-22-22-1-1-12221111-1-2-1-1-12211-211-211-1-100-2-1-11133−3−30033−3−30033−3−3-2-2221111-1-1-1-100000000−3−333000000
χ292222-12-22-22-1-1-12221111-1-2-1-1-12211-211-211-1-100-2-1-111−3−33300−3−33300−3−33322-2-2-1-1-1-1111100000000−3−333000000
χ302222-12-22-22-1-1-12221111-1-2-1-1-12211-211-211-1-100-2-1-111−3−33300−3−33300−3−333-2-2221111-1-1-1-10000000033−3−3000000
χ312-2-22220-2022-2-22-2-20000202-2-22-2000000002-22−202-2002−22−22−22−22−22−22−22−22i−2i002i2i−2i−2i000000−i2i20000−i2i2−i2i2000000
χ322-2-22220-2022-2-22-2-20000202-2-22-2000000002-22−202-2002−22−22−22−22−22−22−22−2−2i2i00−2i−2i2i2i000000i2−i20000i2−i2i2−i2000000
χ332-2-22220-2022-2-22-2-20000202-2-22-2000000002-2−2202-200−22−22−22−22−22−22−22−222i−2i002i2i−2i−2i000000i2−i20000i2−i2i2−i2000000
χ342-2-22220-2022-2-22-2-20000202-2-22-2000000002-2−2202-200−22−22−22−22−22−22−22−22−2i2i00−2i−2i2i2i000000−i2i20000−i2i2−i2i2000000
χ352-2-22-120-202-1112-2-23−33−3-10-1112-23−303−303−3-112−20-113−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232i−2i00−i−iii−i3−i3i3i300−i2i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ362-2-22-120-202-1112-2-23−33−3-10-1112-23−303−303−3-112−20-113−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−2i2i00ii−i−ii3i3−i3−i300i2−i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ372-2-22-120-202-1112-2-23−33−3-10-1112-23−303−303−3-11−220-113−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ232i−2i00−i−iii−i3−i3i3i300i2−i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ382-2-22-120-202-1112-2-23−33−3-10-1112-23−303−303−3-11−220-113−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−2i2i00ii−i−ii3i3−i3−i300−i2i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ392-2-22-120-202-1112-2-2−33−33-10-1112-2−330−330−33-112−20-11−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72i−2i00−i−iiii3i3−i3−i300−i2i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ402-2-22-120-202-1112-2-2−33−33-10-1112-2−330−330−33-112−20-11−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−2i2i00ii−i−i−i3−i3i3i300i2−i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ412-2-22-120-202-1112-2-2−33−33-10-1112-2−330−330−33-11−220-11−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ72i−2i00−i−iiii3i3−i3−i300i2−i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ422-2-22-120-202-1112-2-2−33−33-10-1112-2−330−330−33-11−220-11−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−2i2i00ii−i−i−i3−i3i3i300−i2i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ4344444-2-44-44444-2-2-2-4-4-4-4-2-4-2-2-2-2-2-4-422222244002-2-2220000000000000000000000000000000000000000000000
χ4444444-2-4-4-4-4444-2-2-2-4-4-4-4-24-2-2-22244222222-4-400-222-2-20000000000000000000000000000000000000000000000
χ454444-244-44-4-2-2-2444-2-2-2-2-2-4-2-2-2-4-4224-2-24-2-22200-422220000000000000000000000000000000000000000000000
χ464444-24-4-4-4-4-2-2-24442222-24-2-2-2-4-4-2-2-422-4222200422-2-20000000000000000000000000000000000000000000000
χ474444-2-24444-2-2-2-2-2-2-2-2-2-214111-2-2-2-2-211-211-2-244-21111-2-2-2-2-2-21111-2-21111000000000000000000000000000000
χ484444-2-24444-2-2-2-2-2-2-2-2-2-214111-2-2-2-2-211-211-2-2-4-4-21111222222-1-1-1-122-1-1-1-1000000000000000000000000000000
χ494444-2-24-44-4-2-2-2-2-2-2-2-2-2-21-41112222-211-21122002-1-1-1-10000−2i3−2i3i3i3i3i32i32i3−i3−i3−i3−i3000000000000000000000000000000
χ504444-2-24-44-4-2-2-2-2-2-2-2-2-2-21-41112222-211-21122002-1-1-1-100002i32i3−i3−i3−i3−i3−2i3−2i3i3i3i3i3000000000000000000000000000000
χ514444-2-2-44-44-2-2-2-2-2-222221-4111-2-2222-1-12-1-1-2-200211-1-12323−23−2300−3−33300−3−333000000000000000000000000000000
χ524444-2-2-44-44-2-2-2-2-2-222221-4111-2-2222-1-12-1-1-2-200211-1-1−23−2323230033−3−30033−3−3000000000000000000000000000000
χ534444-2-2-4-4-4-4-2-2-2-2-2-222221411122-2-22-1-12-1-12200-2-1-1110000003i3i−3i−3i00−3i−3i3i3i000000000000000000000000000000
χ544444-2-2-4-4-4-4-2-2-2-2-2-222221411122-2-22-1-12-1-12200-2-1-111000000−3i−3i3i3i003i3i−3i−3i000000000000000000000000000000
χ5544-4-44440-40-44-4-44-444-4-440-44-40000-4-4-44440000000000000000000000000000000000000000000000000000000
χ5644-4-444-4040-44-4-44-4-4-44440-44-40000444-4-4-40000000000000000000000000000000000000000000000000000000
χ5744-4-44-240-40-44-42-2244-4-4-202-220000222-2-2-2000000000000000000000000000000000000000000023−230000000000
χ5844-4-44-240-40-44-42-2244-4-4-202-220000222-2-2-20000000000000000000000000000000000000000000−23230000000000
χ5944-4-44-2-4040-44-42-22-4-444-202-220000-2-2-222200000000000000000000000000000000000000000−2i32i3000000000000
χ6044-4-44-2-4040-44-42-22-4-444-202-220000-2-2-2222000000000000000000000000000000000000000002i3−2i3000000000000
χ6144-4-4-2440-402-22-44-4-2-222-202-220000-4224-2-2000000000000000000000000000006−66−66−66−6000000000000000000
χ6244-4-4-2440-402-22-44-4-2-222-202-220000-4224-2-200000000000000000000000000000−66−66−66−66000000000000000000
χ6344-4-4-24-40402-22-44-422-2-2-202-2200004-2-2-422000000000000000000000000000006−66−6−66−66000000000000000000
χ6444-4-4-24-40402-22-44-422-2-2-202-2200004-2-2-42200000000000000000000000000000−66−666−66−6000000000000000000
χ654-44-4440000-4-44-4-44000040-4-440000000000000000000000000000000000000−2i22i20000−2i22i22i2−2i2000000000000000000
χ664-44-4440000-4-44-4-44000040-4-4400000000000000000000000000000000000002i2−2i200002i2−2i2−2i22i2000000000000000000
χ674-44-4-24000022-2-4-4423−23−2323-2022-200000−2323023−23000000000000000000000000000−2i22i2−i6i6i6−i6i2−i2−i2i2000000000000000000
χ684-44-4-24000022-2-4-4423−23−2323-2022-200000−2323023−230000000000000000000000000002i2−2i2i6−i6−i6i6−i2i2i2−i2000000000000000000
χ694-44-4-24000022-2-4-44−232323−23-2022-20000023−230−2323000000000000000000000000000−2i22i2i6−i6−i6i6i2−i2−i2i2000000000000000000
χ704-44-4-24000022-2-4-44−232323−23-2022-20000023−230−23230000000000000000000000000002i2−2i2−i6i6i6−i6−i2i2i2−i2000000000000000000
χ714-4-4444040-44-4-44-4-40000404-4-4-4400000000-44000-44000000000000000000000000000000000000000000000000
χ724-4-444-2040-44-4-4-2220000-20-2222-200000000-440002-2000000i6−i6i6−i6i6−i6−i6i6−i6i6−i6i6000000000000000000000000000000
χ734-4-444-2040-44-4-4-2220000-20-2222-200000000-440002-2000000−i6i6−i6i6−i6i6i6−i6i6−i6i6−i6000000000000000000000000000000
χ744-4-444-20-4044-4-4-2220000-20-222-22000000004-422−220-220022−2222−22−22−22−22−22−22−22000000000000000000000000000000
χ754-4-444-20-4044-4-4-2220000-20-222-22000000004-4−22220-2200−2222−22222−22−22−22−22−22−2000000000000000000000000000000
χ764-4-44-24040-4-2224-4-423−2323−23-20-222-44−2323023−23023−232-20002-2−23230000000000000000000000000000000000000000000000
χ774-4-44-24040-4-2224-4-4−2323−2323-20-222-4423−230−23230−23232-20002-223−230000000000000000000000000000000000000000000000
χ784-4-44-2-2040-4-222-22223−2323−23101-1-12-2−23230−330−332-2000-113−30000i6−i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−i6i6−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23000000000000000000000000000000
χ794-4-44-2-2040-4-222-22223−2323−23101-1-12-2−23230−330−332-2000-113−30000−i6i6−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23i6−i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23000000000000000000000000000000
χ804-4-44-2-2040-4-222-222−2323−2323101-1-12-223−2303−303−32-2000-11−330000i6−i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−i6i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23000000000000000000000000000000
χ814-4-44-2-2040-4-222-222−2323−2323101-1-12-223−2303−303−32-2000-11−330000−i6i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23i6−i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23000000000000000000000000000000
χ824-4-44-2-20-404-222-22223−2323−23101-1-1-2223−230−330−33-2222−2201-1−332ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000000000000000000000
χ834-4-44-2-20-404-222-22223−2323−23101-1-1-2223−230−330−33-22−222201-1−33−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000000000000000000000
χ844-4-44-2-20-404-222-222−2323−2323101-1-1-22−232303−303−3-2222−2201-13−32ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000000000000000000000
χ854-4-44-2-20-404-222-222−2323−2323101-1-1-22−232303−303−3-22−222201-13−3−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000000000000000000000
χ8688-8-8-4-480-804-444-44-4-44420-22-200004-2-2-4220000000000000000000000000000000000000000000000000000000
χ8788-8-8-4-4-80804-444-4444-4-420-22-20000-4224-2-20000000000000000000000000000000000000000000000000000000
χ888-88-88-40000-8-8844-40000-4044-400000000000000000000000000000000000000000000000000000000000000000
χ898-88-8-4-4000044-444-443−43−434320-2-220000023−230−23230000000000000000000000000000000000000000000000000000000
χ908-88-8-4-4000044-444-4−434343−4320-2-2200000−2323023−230000000000000000000000000000000000000000000000000000000

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