Finite Group Databasebeta

← Group #11781718

Character table — Group #11781718

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222244444444444444444888888888888888888888881212121212121212121212122424242424242424242424244848487272144
order122233444466666612121212346661212121212121212121212128812121212122424242424242424242424242424242488882424242424242424246688121224242424266882
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111-1-1-1
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
χ51111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-111-1
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
χ81111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-1
χ92222222-22-222222222222-22222-2-2-2-222222-2-200-2-2-2-2-200000000000000000000000000002-22200-2-20000000000
χ102222222-22-222222222222-22222-2-2-2-222222-2-200-2-2-2-2-20000000000000000000000000000-22-2-200220000000000
χ11222222-22-22222222-2-2-2-22-2222-2-2-222-2-2-2-2-22200-222-2-2000000000000000022-2-22222-2-2-2-2000000000000000000
χ12222222-22-22222222-2-2-2-22-2222-2-2-222-2-2-2-2-22200-222-2-20000000000000000-2-222-2-2-2-22222000000000000000000
χ13222222-2-2-2-2222222-2-2-2-222222-222-2-2-2-2-2-2-2-2-2002-2-22200000000000000000000000000000000000000000002i−2i0
χ14222222-2-2-2-2222222-2-2-2-222222-222-2-2-2-2-2-2-2-2-2002-2-2220000000000000000000000000000000000000000000−2i2i0
χ1522222-12222222-1-1-12222-12-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-100-1-100002-1-1000
χ1622222-12222222-1-1-12222-12-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-21100110000-211000
χ1722222-12222222-1-1-12222-12-1-1-1-122-1-1-1-1-1-1-122-2-2-1-1-1-1-1-2-2-2-211111111111100000000000022-1-100-1-10000-211000
χ1822222-12222222-1-1-12222-12-1-1-1-122-1-1-1-1-1-1-122-2-2-1-1-1-1-1-2-2-2-2111111111111000000000000-2-211001100002-1-1000
χ1922222-12-22-2222-1-1-12222-1-2-1-1-1-1-2-211-1-1-1-1-1-2-200111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i30000000000002-2-1-1001100000−i3i3000
χ2022222-12-22-2222-1-1-12222-1-2-1-1-1-1-2-211-1-1-1-1-1-2-200111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3000000000000-221100-1-100000i3−i3000
χ2122222-12-22-2222-1-1-12222-1-2-1-1-1-1-2-211-1-1-1-1-1-2-200111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i30000000000002-2-1-1001100000i3−i3000
χ2222222-12-22-2222-1-1-12222-1-2-1-1-1-1-2-211-1-1-1-1-1-2-200111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3000000000000-221100-1-100000−i3i3000
χ232222-122222-1-1-1222-1-1-1-1-12-1-1-12-1-122-1-12-1-1-1-1222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-100002200-1-1-1-1000000
χ242222-122222-1-1-1222-1-1-1-1-12-1-1-12-1-122-1-12-1-1-1-1222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-2111111110000-2-2001111000000
χ252222-122222-1-1-1222-1-1-1-1-12-1-1-12-1-122-1-12-1-1-1-1-2-22-1-1-1-11111-2-21111-2-211112222-1-1-1-1-1-1-1-10000-2-2001111000000
χ262222-122222-1-1-1222-1-1-1-1-12-1-1-12-1-122-1-12-1-1-1-1-2-22-1-1-1-11111-2-21111-2-21111-2-2-2-21111111100002200-1-1-1-1000000
χ272222-12-22-22-1-1-12221111-1-2-1-1-1-2112211-211-1-100-2-1-11133−3−30033−3−30033−3−322-2-2-1-1-1-111110000000033−3−3000000
χ282222-12-22-22-1-1-12221111-1-2-1-1-1-2112211-211-1-100-2-1-11133−3−30033−3−30033−3−3-2-2221111-1-1-1-100000000−3−333000000
χ292222-12-22-22-1-1-12221111-1-2-1-1-1-2112211-211-1-100-2-1-111−3−33300−3−33300−3−33322-2-2-1-1-1-1111100000000−3−333000000
χ302222-12-22-22-1-1-12221111-1-2-1-1-1-2112211-211-1-100-2-1-111−3−33300−3−33300−3−333-2-2221111-1-1-1-10000000033−3−3000000
χ312-2-22220-2022-2-2-2-220000202-2-20002-2000002-22−202-2002−22−22−22−22−22−22−22−2002-2000022-2-200002−2002−22−2000000
χ322-2-22220-2022-2-2-2-220000202-2-20002-2000002-22−202-2002−22−22−22−22−22−22−22−200-220000-2-2220000−2200−22−22000000
χ332-2-22220-2022-2-2-2-220000202-2-20002-2000002-2−2202-200−22−22−22−22−22−22−22−22002-2000022-2-20000−2200−22−22000000
χ342-2-22220-2022-2-2-2-220000202-2-20002-2000002-2−2202-200−22−22−22−22−22−22−22−2200-220000-2-22200002−2002−22−2000000
χ352-2-22-120-202-111-2-223−33−3-10-11103−32-23−303−3-112−20-113−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23002-233−3−3-1-11100002−200ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000
χ362-2-22-120-202-111-2-223−33−3-10-11103−32-23−303−3-112−20-113−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300-22−3−33311-1-10000−2200−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000
χ372-2-22-120-202-111-2-223−33−3-10-11103−32-23−303−3-11−220-113−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23002-233−3−3-1-1110000−2200−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000
χ382-2-22-120-202-111-2-223−33−3-10-11103−32-23−303−3-11−220-113−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300-22−3−33311-1-100002−200ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000
χ392-2-22-120-202-111-2-22−33−33-10-1110−332-2−330−33-112−20-11−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7002-2−3−333-1-11100002−200ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000
χ402-2-22-120-202-111-2-22−33−33-10-1110−332-2−330−33-112−20-11−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700-2233−3−311-1-10000−2200−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000
χ412-2-22-120-202-111-2-22−33−33-10-1110−332-2−330−33-11−220-11−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7002-2−3−333-1-1110000−2200−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000
χ422-2-22-120-202-111-2-22−33−33-10-1110−332-2−330−33-11−220-11−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700-2233−3−311-1-100002−200ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000
χ4344444-2-44-44444-2-2-2-4-4-4-4-2-4-2-2-22-4-4-2-22222244002-2-2220000000000000000000000000000000000000000000000
χ4444444-2-4-4-4-4444-2-2-2-4-4-4-4-24-2-2-22442222222-4-400-222-2-20000000000000000000000000000000000000000000000
χ454444-244-44-4-2-2-2444-2-2-2-2-2-4-2-2-2422-4-4-2-24-2-22200-422220000000000000000000000000000000000000000000000
χ464444-24-4-4-4-4-2-2-24442222-24-2-2-2-4-2-2-4-422-4222200422-2-20000000000000000000000000000000000000000000000
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
χ494444-2-24-44-4-2-2-2-2-2-2-2-2-2-21-4111-2222211-21122002-1-1-1-10000−2i3−2i3i3i3i3i32i32i3−i3−i3−i3−i3000000000000000000000000000000
χ504444-2-24-44-4-2-2-2-2-2-2-2-2-2-21-4111-2222211-21122002-1-1-1-100002i32i3−i3−i3−i3−i3−2i3−2i3i3i3i3i3000000000000000000000000000000
χ514444-2-2-44-44-2-2-2-2-2-222221-4111222-2-2-1-12-1-1-2-200211-1-12323−23−2300−3−33300−3−333000000000000000000000000000000
χ524444-2-2-44-44-2-2-2-2-2-222221-4111222-2-2-1-12-1-1-2-200211-1-1−23−2323230033−3−30033−3−3000000000000000000000000000000
χ534444-2-2-4-4-4-4-2-2-2-2-2-22222141112-2-222-1-12-1-12200-2-1-1110000003i3i−3i−3i00−3i−3i3i3i000000000000000000000000000000
χ544444-2-2-4-4-4-4-2-2-2-2-2-22222141112-2-222-1-12-1-12200-2-1-111000000−3i−3i3i3i003i3i−3i−3i000000000000000000000000000000
χ5544-4-4440000-44-44-4-4000040-44-40000000000000000000000000000000000022−220022−2222−220000000000000000000000
χ5644-4-4440000-44-44-4-4000040-44-400000000000000000000000000000000000−222200−2222−22220000000000000000000000
χ5744-4-4-2400002-224-4-423−23−2323-202-2200000−2323023−23000000000000000000000000022−2200−22−226−66−6000000000000000000
χ5844-4-4-2400002-224-4-423−23−2323-202-2200000−2323023−230000000000000000000000000−2222002−22−2−66−66000000000000000000
χ5944-4-4-2400002-224-4-4−232323−23-202-220000023−230−2323000000000000000000000000022−2200−22−22−66−66000000000000000000
χ6044-4-4-2400002-224-4-4−232323−23-202-220000023−230−23230000000000000000000000000−2222002−22−26−66−6000000000000000000
χ614-44-44440-40-4-44-44-444-4-440-4-44-40000-4-44440000000000000000000000000000000000000000000000000000000
χ624-44-444-4040-4-44-44-4-4-44440-4-444000044-4-4-40000000000000000000000000000000000000000000000000000000
χ634-44-44-240-40-4-442-2244-4-4-2022-22000022-2-2-2000000000000000000000000000000000000000−2i32i300000000000000
χ644-44-44-240-40-4-442-2244-4-4-2022-22000022-2-2-20000000000000000000000000000000000000002i3−2i300000000000000
χ654-44-44-2-4040-4-442-22-4-444-2022-2-20000-2-2222000000000000000000000000000000000000000000023−230000000000
χ664-44-44-2-4040-4-442-22-4-444-2022-2-20000-2-22220000000000000000000000000000000000000000000−23230000000000
χ674-44-4-2440-4022-2-44-4-2-222-2022-2-40000224-2-2000000000000000000000000000006−6−66−666−6000000000000000000
χ684-44-4-2440-4022-2-44-4-2-222-2022-2-40000224-2-200000000000000000000000000000−666−66−6−66000000000000000000
χ694-44-4-24-404022-2-44-422-2-2-2022-240000-2-2-422000000000000000000000000000006−6−666−6−66000000000000000000
χ704-44-4-24-404022-2-44-422-2-2-2022-240000-2-2-42200000000000000000000000000000−666−6−666−6000000000000000000
χ714-4-4444040-44-4-4-4-440000404-4-4000-4400000-44000-44000000000000000000000000000000000000000000000000
χ724-4-444-2040-44-4-422-20000-20-2220002-200000-440002-2000000i6−i6i6−i6i6−i6−i6i6−i6i6−i6i6000000000000000000000000000000
χ734-4-444-2040-44-4-422-20000-20-2220002-200000-440002-2000000−i6i6−i6i6−i6i6i6−i6i6−i6i6−i6000000000000000000000000000000
χ744-4-444-20-4044-4-422-20000-20-222000-22000004-422−220-220022−2222−22−22−22−22−22−22−22000000000000000000000000000000
χ754-4-444-20-4044-4-422-20000-20-222000-22000004-4−22220-2200−2222−22222−22−22−22−22−22−2000000000000000000000000000000
χ764-4-44-24040-4-222-4-4423−2323−23-20-2220−2323-4423−23023−232-20002-2−23230000000000000000000000000000000000000000000000
χ774-4-44-24040-4-222-4-44−2323−2323-20-222023−23-44−23230−23232-20002-223−230000000000000000000000000000000000000000000000
χ784-4-44-2-2040-4-22222-223−2323−23101-1-10−23232-2−330−332-2000-113−30000i6−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
χ794-4-44-2-2040-4-22222-223−2323−23101-1-10−23232-2−330−332-2000-113−30000−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
χ804-4-44-2-2040-4-22222-2−2323−2323101-1-1023−232-23−303−32-2000-11−330000i6−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
χ814-4-44-2-2040-4-22222-2−2323−2323101-1-1023−232-23−303−32-2000-11−330000−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
χ824-4-44-2-20-404-22222-223−2323−23101-1-1023−23-22−330−33-2222−2201-1−332ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000000000000000000000
χ834-4-44-2-20-404-22222-223−2323−23101-1-1023−23-22−330−33-22−222201-1−33−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000000000000000000000
χ844-4-44-2-20-404-22222-2−2323−2323101-1-10−2323-223−303−3-2222−2201-13−32ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000000000000000000000
χ854-4-44-2-20-404-22222-2−2323−2323101-1-10−2323-223−303−3-22−222201-13−3−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000000000000000000000
χ8688-8-88-40000-88-8-4440000-404-4400000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8-4-400004-44-44443−43−434320-22-20000023−230−23230000000000000000000000000000000000000000000000000000000
χ8888-8-8-4-400004-44-444−434343−4320-22-200000−2323023−230000000000000000000000000000000000000000000000000000000
χ898-88-8-4-480-8044-44-44-4-44420-2-2240000-2-2-4220000000000000000000000000000000000000000000000000000000
χ908-88-8-4-4-808044-44-4444-4-420-2-22-40000224-2-20000000000000000000000000000000000000000000000000000000

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