Finite Group Databasebeta

← Group #11792770

Character table — Group #11792770

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1111222222222222222222444444444444444444888888888888888888888812121212121212121212121224242424242424242424242424242424242472727272
order12222233444466666612121212366666661212121212121212121224666666666612121212121212121212888824242424242424244488881212121224242424242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1
χ922222222-2-2-2-2222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-20000002200000000-2-20000000000000000002i−2i0000002i2i−2i−2i00000000
χ1022222222-2-2-2-2222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-20000002200000000-2-2000000000000000000−2i2i000000−2i−2i2i2i00000000
χ112222222-1222222-1-12-12222-122-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000000000220022-1-1-1-10000-1-1-1-10000
χ122222222-1222222-1-12-12222-122-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000000000-2-200-2-21111000011110000
χ132222222-1222222-1-12-12222-122-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211-1-11111-2-211-1-111110000000000002200-2-2-1-1-1-1000011110000
χ142222222-1222222-1-12-12222-122-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211-1-11111-2-211-1-11111000000000000-2-2002211110000-1-1-1-10000
χ15222222-122222-1-122-12-1-1-1-1-1-1-122-1-1-1-1-1222-1-1-1-1222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-10022000000-1-1-1-100000000
χ16222222-122222-1-122-12-1-1-1-1-1-1-122-1-1-1-1-1222-1-1-1-1222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-21111111100-2-2000000111100000000
χ17222222-122222-1-122-12-1-1-1-1-1-1-122-1-1-1-1-1222-1-1-1-12-2-211-2-2-1-1111111-2-2-1-111112222-1-1-1-1-1-1-1-100-2-2000000111100000000
χ18222222-122222-1-122-12-1-1-1-1-1-1-122-1-1-1-1-1222-1-1-1-12-2-211-2-2-1-1111111-2-2-1-11111-2-2-2-2111111110022000000-1-1-1-100000000
χ19222222-12-2-2-2-2-1-122-121111-1-1-122-1-1-111-2-2-21111-200−i3i300-1-1−i3−i3i3i3−i3i30011−i3−i3i3i300003333−3−3−3−3002i−2i000000−i−iii00000000
χ20222222-12-2-2-2-2-1-122-121111-1-1-122-1-1-111-2-2-21111-200−i3i300-1-1−i3−i3i3i3−i3i30011−i3−i3i3i30000−3−3−3−3333300−2i2i000000ii−i−i00000000
χ21222222-12-2-2-2-2-1-122-121111-1-1-122-1-1-111-2-2-21111-200i3−i300-1-1i3i3−i3−i3i3−i30011i3i3−i3−i300003333−3−3−3−300−2i2i000000ii−i−i00000000
χ22222222-12-2-2-2-2-1-122-121111-1-1-122-1-1-111-2-2-21111-200i3−i300-1-1i3i3−i3−i3i3−i30011i3i3−i3−i30000−3−3−3−33333002i−2i000000−i−iii00000000
χ232222-2-22222-2-222222222222-2-2-2-2222-2-222-22222-2000000-2-200000000-2-2000022-2-222-2-222-2-20000000000000000000000
χ242222-2-22222-2-222222222222-2-2-2-2222-2-222-22222-2000000-2-200000000-2-20000-2-222-2-222-2-2220000000000000000000000
χ252222-2-222-2-222222222-2-2-2-22-2-2-2-222222-2-22-2-2-2-222-22222-2-22222-2-2-2-222-2-2-2-20000000000000000000000000000000000
χ262222-2-222-2-222222222-2-2-2-22-2-2-2-222222-2-22-2-2-2-22-22-2-2-2-2-2-2-2-2-2-222222222220000000000000000000000000000000000
χ272222-2-22-1-2-22222-1-12-1-2-2-2-2-1-2-211-1-1-12211-11111-12-222-1-111-1-1-1-1-2-211-1-11111000000000000000000−i3−i3i3i30000−i3−i3i3i30000
χ282222-2-22-1-2-22222-1-12-1-2-2-2-2-1-2-211-1-1-12211-11111-12-222-1-111-1-1-1-1-2-211-1-11111000000000000000000i3i3−i3−i30000i3i3−i3−i30000
χ292222-2-22-1-2-22222-1-12-1-2-2-2-2-1-2-211-1-1-12211-11111-1-22-2-21111111122-1-1-1-1-1-1-1-1000000000000000000−i3−i3i3i30000i3i3−i3−i30000
χ302222-2-22-1-2-22222-1-12-1-2-2-2-2-1-2-211-1-1-12211-11111-1-22-2-21111111122-1-1-1-1-1-1-1-1000000000000000000i3i3−i3−i30000−i3−i3i3i30000
χ312222-2-2-1222-2-2-1-122-12-1-1-1-1-111-2-2-1-1-11122-2-1-1-1-1-200−i3i30011−i3−i3i3i3i3−i30011i3i3−i3−i322-2-2-1-111-1-1110000000000−i3i3−i3i300000000
χ322222-2-2-1222-2-2-1-122-12-1-1-1-1-111-2-2-1-1-11122-2-1-1-1-1-200−i3i30011−i3−i3i3i3i3−i30011i3i3−i3−i3-2-22211-1-111-1-10000000000i3−i3i3−i300000000
χ332222-2-2-1222-2-2-1-122-12-1-1-1-1-111-2-2-1-1-11122-2-1-1-1-1-200i3−i30011i3i3−i3−i3−i3i30011−i3−i3i3i322-2-2-1-111-1-1110000000000i3−i3i3−i300000000
χ342222-2-2-1222-2-2-1-122-12-1-1-1-1-111-2-2-1-1-11122-2-1-1-1-1-200i3−i30011i3i3−i3−i3−i3i30011−i3−i3i3i3-2-22211-1-111-1-10000000000−i3i3−i3i300000000
χ352222-2-2-12-2-222-1-122-121111-111-2-2-1-1-1-1-1-2-22111122-2-1-12211-1-1-1-111-2-2-1-11111000033−3−3−3−33300000000003−3−3300000000
χ362222-2-2-12-2-222-1-122-121111-111-2-2-1-1-1-1-1-2-22111122-2-1-12211-1-1-1-111-2-2-1-111110000−3−33333−3−30000000000−333−300000000
χ372222-2-2-12-2-222-1-122-121111-111-2-2-1-1-1-1-1-2-2211112-2211-2-2111111-1-122-1-1-1-1-1-1000033−3−3−3−3330000000000−333−300000000
χ382222-2-2-12-2-222-1-122-121111-111-2-2-1-1-1-1-1-2-2211112-2211-2-2111111-1-122-1-1-1-1-1-10000−3−33333−3−300000000003−3−3300000000
χ392-2-222-2222-22-2-2-2-2-22222-2-222-22-2-2-222-22-2-222-2-220000002-2000000002-200000000000000002-200002-22-2000000000000
χ402-2-222-2222-22-2-2-2-2-22222-2-222-22-2-2-222-22-2-222-2-220000002-2000000002-20000000000000000-220000-22-22000000000000
χ412-2-222-222-22-22-2-2-2-222-2-22222-22-2-2-22-22-222-2-222-20000002-200000000-220000000000000000000000000000000000002-2
χ422-2-222-222-22-22-2-2-2-222-2-22222-22-2-2-22-22-222-2-222-20000002-200000000-22000000000000000000000000000000000000-22
χ432-2-222-22-12-22-2-2-2112-122-2-2-12-2-1111-12-2-111-1-111-10000−i3i3-11−i3i3−i3i300−i3i3-11−i3i3−i3i30000000000002-20000-11-110000−i3i3−i3i30000
χ442-2-222-22-12-22-2-2-2112-122-2-2-12-2-1111-12-2-111-1-111-10000−i3i3-11−i3i3−i3i300−i3i3-11−i3i3−i3i3000000000000-2200001-11-10000i3−i3i3−i30000
χ452-2-222-22-12-22-2-2-2112-122-2-2-12-2-1111-12-2-111-1-111-10000i3−i3-11i3−i3i3−i300i3−i3-11i3−i3i3−i30000000000002-20000-11-110000i3−i3i3−i30000
χ462-2-222-22-12-22-2-2-2112-122-2-2-12-2-1111-12-2-111-1-111-10000i3−i3-11i3−i3i3−i300i3−i3-11i3−i3i3−i3000000000000-2200001-11-10000−i3i3−i3i30000
χ472-2-22-22222-2-22-2-2-2-22222-2-22-22-22-2-22-222-2222-2-2-2000000-2200000000-2200000000000000000000000000000000002-200
χ482-2-22-22222-2-22-2-2-2-22222-2-22-22-22-2-22-222-2222-2-2-2000000-2200000000-220000000000000000000000000000000000-2200
χ492-2-22-2222-222-2-2-2-2-222-2-2222-22-22-2-222-2-22-2-2-2222000000-22000000002-2000000000000000000002-2000000002-2-220000
χ502-2-22-2222-222-2-2-2-2-222-2-2222-22-22-2-222-2-22-2-2-2222000000-22000000002-200000000000000000000-2200000000-222-20000
χ512-2-22-222-1-222-2-2-2112-1-2-222-1-221-111-12-21-1111-1-1-10000−i3i31-1−i3i3−i3i300i3−i3-11i3−i3i3−i300000000000000002-2−i3i3i3−i30000-111-10000
χ522-2-22-222-1-222-2-2-2112-1-2-222-1-221-111-12-21-1111-1-1-10000−i3i31-1−i3i3−i3i300i3−i3-11i3−i3i3−i30000000000000000-22i3−i3−i3i300001-1-110000
χ532-2-22-222-1-222-2-2-2112-1-2-222-1-221-111-12-21-1111-1-1-10000i3−i31-1i3−i3i3−i300−i3i3-11−i3i3−i3i300000000000000002-2i3−i3−i3i30000-111-10000
χ542-2-22-222-1-222-2-2-2112-1-2-222-1-221-111-12-21-1111-1-1-10000i3−i31-1i3−i3i3−i300−i3i3-11−i3i3−i3i30000000000000000-22−i3i3i3−i300001-1-110000
χ554444444-2-4-4-4-444-2-24-2-4-4-4-4-244-2-2-2-2-2-4-422222222000000-2-2000000002200000000000000000000000000000000000000
χ56444444-2-24444-2-2-2-2-2-2-2-2-2-21-2-2-2-2111-2-2-2-2-21111-244-2-2-2-2111111-2-2-2-21111110000000000000000000000000000000000
χ57444444-2-24444-2-2-2-2-2-2-2-2-2-21-2-2-2-2111-2-2-2-2-21111-2-4-4222211-1-1-1-1222211-1-1-1-10000000000000000000000000000000000
χ58444444-2-2-4-4-4-4-2-2-2-2-2-222221-2-2-2-211122222-1-1-1-1200−2i32i30011i3i3−i3−i3−2i32i300-1-1i3i3−i3−i30000000000000000000000000000000000
χ59444444-2-2-4-4-4-4-2-2-2-2-2-222221-2-2-2-211122222-1-1-1-12002i3−2i30011−i3−i3i3i32i3−2i300-1-1−i3−i3i3i30000000000000000000000000000000000
χ604444-4-44-244-4-444-2-24-24444-2-4-422-2-2-2-4-4-2-22-2-2-2-2200000022000000002200000000000000000000000000000000000000
χ614444-4-4-2-244-4-4-2-2-2-2-2-2-2-2-2-21222211122-2-221111200−2i32i300-1-1i3i3−i3−i32i3−2i300-1-1−i3−i3i3i30000000000000000000000000000000000
χ624444-4-4-2-244-4-4-2-2-2-2-2-2-2-2-2-21222211122-2-2211112002i3−2i300-1-1−i3−i3i3i3−2i32i300-1-1i3i3−i3−i30000000000000000000000000000000000
χ634444-4-4-2-2-4-444-2-2-2-2-2-2222212222111-2-222-2-1-1-1-1-24-4-2-2-2-2-1-11111222211-1-1-1-10000000000000000000000000000000000
χ644444-4-4-2-2-4-444-2-2-2-2-2-2222212222111-2-222-2-1-1-1-1-2-442222-1-1-1-1-1-1-2-2-2-21111110000000000000000000000000000000000
χ6544-4-4004400004-44-4-4-40000400004-4-4000000000000000000000000000000000022−220022−220022−220000000000000000000000
χ6644-4-4004400004-44-4-4-40000400004-4-40000000000000000000000000000000000−222200−222200−22220000000000000000000000
χ6744-4-400-240000-224-42-423−2323−23-20000-2220000023−2323−23000000000000000000000000022−22002ζ13−2ζ23−2ζ13+2ζ23002ζ5−2ζ7−2ζ5+2ζ70000000000000000000000
χ6844-4-400-240000-224-42-423−2323−23-20000-2220000023−2323−230000000000000000000000000−222200−2ζ13+2ζ232ζ13−2ζ2300−2ζ5+2ζ72ζ5−2ζ70000000000000000000000
χ6944-4-400-240000-224-42-4−2323−2323-20000-22200000−2323−2323000000000000000000000000022−22002ζ5−2ζ7−2ζ5+2ζ7002ζ13−2ζ23−2ζ13+2ζ230000000000000000000000
χ7044-4-400-240000-224-42-4−2323−2323-20000-22200000−2323−23230000000000000000000000000−222200−2ζ5+2ζ72ζ5−2ζ700−2ζ13+2ζ232ζ13−2ζ230000000000000000000000
χ714-44-400440000-44-44-4-4000040000-44-40000000000000000000000000000000022−220022−220022−22000000000000000000000000
χ724-44-400440000-44-44-4-4000040000-44-400000000000000000000000000000000−222200−222200−2222000000000000000000000000
χ734-44-400-2400002-2-442-423−23−2323-200002-220000023−23−23230000000000000000000000022−22002ζ13−2ζ23−2ζ13+2ζ23002ζ5−2ζ7−2ζ5+2ζ7000000000000000000000000
χ744-44-400-2400002-2-442-423−23−2323-200002-220000023−23−232300000000000000000000000−222200−2ζ13+2ζ232ζ13−2ζ2300−2ζ5+2ζ72ζ5−2ζ7000000000000000000000000
χ754-44-400-2400002-2-442-4−232323−23-200002-2200000−232323−230000000000000000000000022−22002ζ5−2ζ7−2ζ5+2ζ7002ζ13−2ζ23−2ζ13+2ζ23000000000000000000000000
χ764-44-400-2400002-2-442-4−232323−23-200002-2200000−232323−2300000000000000000000000−222200−2ζ5+2ζ72ζ5−2ζ700−2ζ13+2ζ232ζ13−2ζ23000000000000000000000000
χ774-4-444-44-2-44-44-4-4224-2-4-444-24-4-2222-2-442-2-222-2-22000000-22000000002-200000000000000000000000000000000000000
χ784-4-444-4-244-44-422-4-4-24-2-222-2-224-422-2-224-4-4-2-2224000000-2200000000-2200000000000000000000000000000000000000
χ794-4-444-4-24-44-4422-4-4-2422-2-2-2-224-422-22-2-44422-2-2-4000000-22000000002-200000000000000000000000000000000000000
χ804-4-444-4-2-24-44-42222-2-2-2-2221-22-22-1-11-22-22211-1-1-20000−2i32i31-1i3−i3i3−i300−2i32i31-1i3−i3i3−i30000000000000000000000000000000000
χ814-4-444-4-2-24-44-42222-2-2-2-2221-22-22-1-11-22-22211-1-1-200002i3−2i31-1−i3i3−i3i3002i3−2i31-1−i3i3−i3i30000000000000000000000000000000000
χ824-4-444-4-2-2-44-442222-2-222-2-21-22-22-1-112-22-2-2-1-11120000001-13-3-330000-113-3-330000000000000000000000000000000000
χ834-4-444-4-2-2-44-442222-2-222-2-21-22-22-1-112-22-2-2-1-11120000001-1-333-30000-11-333-30000000000000000000000000000000000
χ844-4-44-444-24-4-44-4-4224-244-4-4-2-442-222-2-44-22-2-2-22220000002-2000000002-200000000000000000000000000000000000000
χ854-4-44-44-244-4-4422-4-4-24-2-222-22-2-4422-22-24-44-2-222-40000002-2000000002-200000000000000000000000000000000000000
χ864-4-44-44-24-444-422-4-4-2422-2-2-22-2-4422-2-22-44-422-2-240000002-200000000-2200000000000000000000000000000000000000
χ874-4-44-44-2-24-4-442222-2-2-2-22212-22-2-1-112-2-22-211-1-12000000-113-3-330000-11-333-30000000000000000000000000000000000
χ884-4-44-44-2-24-4-442222-2-2-2-22212-22-2-1-112-2-22-211-1-12000000-11-333-30000-113-3-330000000000000000000000000000000000
χ894-4-44-44-2-2-444-42222-2-222-2-212-22-2-1-11-222-22-1-111-20000−2i32i3-11i3−i3i3−i3002i3−2i31-1−i3i3−i3i30000000000000000000000000000000000
χ904-4-44-44-2-2-444-42222-2-222-2-212-22-2-1-11-222-22-1-111-200002i3−2i3-11−i3i3−i3i300−2i32i31-1i3−i3i3−i30000000000000000000000000000000000
χ9188-8-8008-400008-8-44-840000-40000-444000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-800-4-40000-44-444443−4343−43200002-2-200000−2323−2323000000000000000000000000000000000000000000000000000000000
χ9388-8-800-4-40000-44-4444−4343−4343200002-2-20000023−2323−23000000000000000000000000000000000000000000000000000000000
χ948-88-8008-40000-884-4-840000-400004-44000000000000000000000000000000000000000000000000000000000000000000
χ958-88-800-4-400004-44-44443−43−434320000-22-200000−232323−23000000000000000000000000000000000000000000000000000000000
χ968-88-800-4-400004-44-444−434343−4320000-22-20000023−23−2323000000000000000000000000000000000000000000000000000000000

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