Finite Group Databasebeta

← Group #11781640

Character table — Group #11781640

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222244444444444444444888888888888888888888881212121212121212121212122424242424242424242424244848487272144
order12223344446666661212121234666121212121212121212121212881212121212242424242424242424242424242424248888242424242424242488882424242424242424266244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111-1-1-1
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
χ51111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-111-1
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
χ81111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111-1
χ92222222-22-222222222222-22222-2-2-222222-2-2-200-2-2-2-2-200000000000000000000000000000000000000000002-20
χ102222222-22-222222222222-22222-2-2-222222-2-2-200-2-2-2-2-20000000000000000000000000000000000000000000-220
χ11222222-22-22222222-2-2-2-22-2222-22-2-2-2-2-2-2-222200-222-2-2000000000000000022-2-22222-2-2-2-2000000000000000000
χ12222222-22-22222222-2-2-2-22-2222-22-2-2-2-2-2-2-222200-222-2-20000000000000000-2-222-2-2-2-22222000000000000000000
χ13222222-2-2-2-2222222-2-2-2-222222-2-222-2-2-2-2-2-2-2-2002-2-2220000000000000000000000000000002i−2i00002i2i−2i−2i000000
χ14222222-2-2-2-2222222-2-2-2-222222-2-222-2-2-2-2-2-2-2-2002-2-222000000000000000000000000000000−2i2i0000−2i−2i2i2i000000
χ1522222-12222222-1-1-12222-12-1-1-1-1-122-1-1-1-1-122-122-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000220000-1-1-1-12-1-1000
χ1622222-12222222-1-1-12222-12-1-1-1-1-122-1-1-1-1-122-122-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000-2-200001111-211000
χ1722222-12222222-1-1-12222-12-1-1-1-1-122-1-1-1-1-122-1-2-2-1-1-1-1-1-2-2-2-211111111111100000000000000220000-1-1-1-1-211000
χ1822222-12222222-1-1-12222-12-1-1-1-1-122-1-1-1-1-122-1-2-2-1-1-1-1-1-2-2-2-211111111111100000000000000-2-2000011112-1-1000
χ1922222-1-2-2-2-2222-1-1-1-2-2-2-2-12-1-1-1112211111-2-2100-111-1-10000333333−3−3−3−3−3−3000000000000002i−2i0000−i−iii0−i3i3000
χ2022222-1-2-2-2-2222-1-1-1-2-2-2-2-12-1-1-1112211111-2-2100-111-1-10000333333−3−3−3−3−3−300000000000000−2i2i0000ii−i−i0i3−i3000
χ2122222-1-2-2-2-2222-1-1-1-2-2-2-2-12-1-1-1112211111-2-2100-111-1-10000−3−3−3−3−3−3333333000000000000002i−2i0000−i−iii0i3−i3000
χ2222222-1-2-2-2-2222-1-1-1-2-2-2-2-12-1-1-1112211111-2-2100-111-1-10000−3−3−3−3−3−333333300000000000000−2i2i0000ii−i−i0−i3i3000
χ232222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12200-1-1-1-10000000000
χ242222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-211111111-2-20011110000000000
χ252222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-1-1-12-1-1-1-12-2-22-1-1-1-11111-2-21111-2-211112222-1-1-1-1-1-1-1-1-2-20011110000000000
χ262222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-1-1-12-1-1-1-12-2-22-1-1-1-11111-2-21111-2-21111-2-2-2-2111111112200-1-1-1-10000000000
χ272222-12-22-22-1-1-12221111-1-2-1-1-1-221111-211-1-1200-2-1-11133−3−30033−3−30033−3−322-2-2-1-1-1-11111000033−3−30000000000
χ282222-12-22-22-1-1-12221111-1-2-1-1-1-221111-211-1-1200-2-1-11133−3−30033−3−30033−3−3-2-2221111-1-1-1-10000−3−3330000000000
χ292222-12-22-22-1-1-12221111-1-2-1-1-1-221111-211-1-1200-2-1-111−3−33300−3−33300−3−33322-2-2-1-1-1-111110000−3−3330000000000
χ302222-12-22-22-1-1-12221111-1-2-1-1-1-221111-211-1-1200-2-1-111−3−33300−3−33300−3−333-2-2221111-1-1-1-1000033−3−30000000000
χ312-2-22220-2022-2-22-2-20000202-2-20-200000002-222−202-2002−22−22−22−22−22−22−22−2002-2000022-2-22−2002−22−20000000000
χ322-2-22220-2022-2-22-2-20000202-2-20-200000002-222−202-2002−22−22−22−22−22−22−22−200-220000-2-222−2200−22−220000000000
χ332-2-22220-2022-2-22-2-20000202-2-20-200000002-22−2202-200−22−22−22−22−22−22−22−22002-2000022-2-2−2200−22−220000000000
χ342-2-22220-2022-2-22-2-20000202-2-20-200000002-22−2202-200−22−22−22−22−22−22−22−2200-220000-2-2222−2002−22−20000000000
χ352-2-22-120-202-1112-2-23−33−3-10-1110-23−33−303−3-1122−20-113−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23002-233−3−3-1-1112−200ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000
χ362-2-22-120-202-1112-2-23−33−3-10-1110-23−33−303−3-1122−20-113−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300-22−3−33311-1-1−2200−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000
χ372-2-22-120-202-1112-2-23−33−3-10-1110-23−33−303−3-112−220-113−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23002-233−3−3-1-111−2200−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000
χ382-2-22-120-202-1112-2-23−33−3-10-1110-23−33−303−3-112−220-113−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300-22−3−33311-1-12−200ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000
χ392-2-22-120-202-1112-2-2−33−33-10-1110-2−33−330−33-1122−20-11−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7002-2−3−333-1-1112−200ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000
χ402-2-22-120-202-1112-2-2−33−33-10-1110-2−33−330−33-1122−20-11−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700-2233−3−311-1-1−2200−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000
χ412-2-22-120-202-1112-2-2−33−33-10-1110-2−33−330−33-112−220-11−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7002-2−3−333-1-111−2200−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000
χ422-2-22-120-202-1112-2-2−33−33-10-1110-2−33−330−33-112−220-11−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700-2233−3−311-1-12−200ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000
χ4344444-24-44-4444-2-2-24444-2-4-2-2-2-22-4-4-2-2-2-2-2-4-4200222220000000000000000000000000000000000000000000000
χ4444444-2-44-44444-2-2-2-4-4-4-4-2-4-2-2-22-2-4-42222244-2002-2-2220000000000000000000000000000000000000000000000
χ454444-244-44-4-2-2-2444-2-2-2-2-2-4-2-2-24-422-2-24-2-222-400-422220000000000000000000000000000000000000000000000
χ464444-24-4-4-4-4-2-2-24442222-24-2-2-2-4-4-2-222-42222-400422-2-20000000000000000000000000000000000000000000000
χ474444-2-24444-2-2-2-2-2-2-2-2-2-214111-2-2-2-211-211-2-2-244-21111-2-2-2-2-2-21111-2-21111000000000000000000000000000000
χ484444-2-24444-2-2-2-2-2-2-2-2-2-214111-2-2-2-211-211-2-2-2-4-4-21111222222-1-1-1-122-1-1-1-1000000000000000000000000000000
χ494444-2-24-44-4-2-2-2-2-2-2-2-2-2-21-4111-222211-211222002-1-1-1-100000033-3-300-3-333000000000000000000000000000000
χ504444-2-24-44-4-2-2-2-2-2-2-2-2-2-21-4111-222211-211222002-1-1-1-1000000-3-3330033-3-3000000000000000000000000000000
χ514444-2-2-44-44-2-2-2-2-2-222221-41112-222-1-12-1-1-2-2-200211-1-12323−23−2300−3−33300−3−333000000000000000000000000000000
χ524444-2-2-44-44-2-2-2-2-2-222221-41112-222-1-12-1-1-2-2-200211-1-1−23−2323230033−3−30033−3−3000000000000000000000000000000
χ534444-2-2-4-4-4-4-2-2-2-2-2-222221411122-2-2-1-12-1-122200-2-1-11100002323−3−3−3−3−23−233333000000000000000000000000000000
χ544444-2-2-4-4-4-4-2-2-2-2-2-222221411122-2-2-1-12-1-122200-2-1-1110000−23−2333332323−3−3−3−3000000000000000000000000000000
χ5544-4-4440000-44-4-44-4000040-44-400000000000000000000000000000000000−2i22i200−2i22i2−2i22i20000000000000000000000
χ5644-4-4440000-44-4-44-4000040-44-4000000000000000000000000000000000002i2−2i2002i2−2i22i2−2i20000000000000000000000
χ5744-4-4-2400002-22-44-423−23−2323-202-22000023−230−232300000000000000000000000000−2i22i200i2−i2i2−i2i6−i6i6−i6000000000000000000
χ5844-4-4-2400002-22-44-423−23−2323-202-22000023−230−2323000000000000000000000000002i2−2i200−i2i2−i2i2−i6i6−i6i6000000000000000000
χ5944-4-4-2400002-22-44-4−232323−23-202-220000−2323023−2300000000000000000000000000−2i22i200i2−i2i2−i2−i6i6−i6i6000000000000000000
χ6044-4-4-2400002-22-44-4−232323−23-202-220000−2323023−23000000000000000000000000002i2−2i200−i2i2−i2i2i6−i6i6−i6000000000000000000
χ614-44-44440-40-4-44-4-4444-4-440-4-44400044-4-4-400000000000000000000000000000000000000000000000000000000
χ624-44-444-4040-4-44-4-44-4-44440-4-44-4000-4-444400000000000000000000000000000000000000000000000000000000
χ634-44-44-240-40-4-4422-244-4-4-2022-2-2000-2-222200000000000000000000000000000000000000000000006−66−6000000
χ644-44-44-240-40-4-4422-244-4-4-2022-2-2000-2-22220000000000000000000000000000000000000000000000−66−66000000
χ654-44-44-2-4040-4-4422-2-4-444-2022-2200022-2-2-20000000000000000000000000000000000000000000000i6−i6−i6i6000000
χ664-44-44-2-4040-4-4422-2-4-444-2022-2200022-2-2-20000000000000000000000000000000000000000000000−i6i6i6−i6000000
χ674-44-4-2440-4022-2-4-44-2-222-2022-24000-2-2-422000000000000000000000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000
χ684-44-4-2440-4022-2-4-44-2-222-2022-24000-2-2-422000000000000000000000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000
χ694-44-4-24-404022-2-4-4422-2-2-2022-2-4000224-2-2000000000000000000000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000
χ704-44-4-24-404022-2-4-4422-2-2-2022-2-4000224-2-2000000000000000000000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000
χ714-4-4444040-44-4-44-4-40000404-4-4040000000-44-4000-44000000000000000000000000000000000000000000000000
χ724-4-444-2040-44-4-4-2220000-20-2220-20000000-4420002-20000006−66−66−6−66−66−66000000000000000000000000000000
χ734-4-444-2040-44-4-4-2220000-20-2220-20000000-4420002-2000000−66−66−666−66−66−6000000000000000000000000000000
χ744-4-444-20-4044-4-4-2220000-20-2220200000004-4-222−220-220022−2222−22−22−22−22−22−22−22000000000000000000000000000000
χ754-4-444-20-4044-4-4-2220000-20-2220200000004-4-2−22220-2200−2222−22222−22−22−22−22−22−2000000000000000000000000000000
χ764-4-44-24040-4-2224-4-423−2323−23-20-22204−232323−23023−232-2-40002-2−23230000000000000000000000000000000000000000000000
χ774-4-44-24040-4-2224-4-4−2323−2323-20-2220423−23−23230−23232-2-40002-223−230000000000000000000000000000000000000000000000
χ784-4-44-2-2040-4-222-22223−2323−23101-1-10-2−2323−330−332-22000-113−300006−6ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23−66−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23000000000000000000000000000000
χ794-4-44-2-2040-4-222-22223−2323−23101-1-10-2−2323−330−332-22000-113−30000−66−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ236−6ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23000000000000000000000000000000
χ804-4-44-2-2040-4-222-222−2323−2323101-1-10-223−233−303−32-22000-11−3300006−6−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23−662ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ23000000000000000000000000000000
χ814-4-44-2-2040-4-222-222−2323−2323101-1-10-223−233−303−32-22000-11−330000−662ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ236−6−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23000000000000000000000000000000
χ824-4-44-2-20-404-222-22223−2323−23101-1-10223−23−330−33-22-222−2201-1−332ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000000000000000000000
χ834-4-44-2-20-404-222-22223−2323−23101-1-10223−23−330−33-22-2−222201-1−33−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000000000000000000000
χ844-4-44-2-20-404-222-222−2323−2323101-1-102−23233−303−3-22-222−2201-13−32ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000000000000000000000
χ854-4-44-2-20-404-222-222−2323−2323101-1-102−23233−303−3-22-2−222201-13−3−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000000000000000000000
χ8688-8-88-40000-88-84-440000-404-4400000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8-4-400004-444-4443−43−434320-22-20000−2323023−2300000000000000000000000000000000000000000000000000000000
χ8888-8-8-4-400004-444-44−434343−4320-22-2000023−230−232300000000000000000000000000000000000000000000000000000000
χ898-88-8-4-480-8044-444-4-4-44420-2-22-4000224-2-200000000000000000000000000000000000000000000000000000000
χ908-88-8-4-4-808044-444-444-4-420-2-224000-2-2-42200000000000000000000000000000000000000000000000000000000

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