Finite Group Databasebeta

← Group #11792744

Character table — Group #11792744

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1111222222222222222222444444444444444444888888888888888888888812121212121212121212121224242424242424242424242424242424242472727272
order1222223344446666661212121236666666121212121212121212126688121224242424242424242424242424242424888824242424242424242224666666881212242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111-1-11111-1-1-1-1
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
χ5111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-111-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111
χ7111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111
χ8111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-11111111111-1-1
χ922222222-2-2-2-2222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2222i−2i-2-22i2i−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i0000000000000000000000000000000000
χ1022222222-2-2-2-2222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-222−2i2i-2-2−2i−2i2i2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i0000000000000000000000000000000000
χ112222222-1222222-1-1-122222-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000022000-1-1-1-12200-1-1-1-10000
χ122222222-1222222-1-1-122222-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000-2-20001111-2-20011110000
χ132222222-1222222-1-1-122222-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-1-1-2-2-2-2111111111111000000000000022000-1-1-1-1-2-20011110000
χ142222222-1222222-1-1-122222-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-1-1-2-2-2-21111111111110000000000000-2-200011112200-1-1-1-10000
χ152222222-1-2-2-2-222-1-1-12-2-2-2-2-122-1-1-1-1-111-2-2111111-1-12i−2i112i2i−2i−2i−i−i−i−i−i−iiiiiii000000000000000000−i3−i3i3i3000033−3−30000
χ162222222-1-2-2-2-222-1-1-12-2-2-2-2-122-1-1-1-1-111-2-2111111-1-12i−2i112i2i−2i−2i−i−i−i−i−i−iiiiiii000000000000000000i3i3−i3−i30000−3−3330000
χ172222222-1-2-2-2-222-1-1-12-2-2-2-2-122-1-1-1-1-111-2-2111111-1-1−2i2i11−2i−2i2i2iiiiiii−i−i−i−i−i−i000000000000000000−i3−i3i3i30000−3−3330000
χ182222222-1-2-2-2-222-1-1-12-2-2-2-2-122-1-1-1-1-111-2-2111111-1-1−2i2i11−2i−2i2i2iiiiiii−i−i−i−i−i−i000000000000000000i3i3−i3−i3000033−3−30000
χ19222222-122222-1-1222-1-1-1-1-1-1-1-122-1-1-122-1-1-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12002-1-1000000-1-100000000
χ20222222-122222-1-1222-1-1-1-1-1-1-1-122-1-1-122-1-1-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-211111111-200-2110000001100000000
χ21222222-122222-1-1222-1-1-1-1-1-1-1-122-1-1-122-1-1-1-12-1-12-1-1-2-2-1-11111-2-21111-2-211112222-1-1-1-1-1-1-1-1-200-2110000001100000000
χ22222222-122222-1-1222-1-1-1-1-1-1-1-122-1-1-122-1-1-1-12-1-12-1-1-2-2-1-11111-2-21111-2-21111-2-2-2-2111111112002-1-1000000-1-100000000
χ23222222-12-2-2-2-2-1-1222-11111-1-1-122-1-1-1-2-21111-211-2-1-12i−2i11−i−iii2i2i−i−i−i−i−2i−2iiiii00003333−3−3−3−30000−i3i3000000−i3i300000000
χ24222222-12-2-2-2-2-1-1222-11111-1-1-122-1-1-1-2-21111-211-2-1-12i−2i11−i−iii2i2i−i−i−i−i−2i−2iiiii0000−3−3−3−333330000i3−i3000000i3−i300000000
χ25222222-12-2-2-2-2-1-1222-11111-1-1-122-1-1-1-2-21111-211-2-1-1−2i2i11ii−i−i−2i−2iiiii2i2i−i−i−i−i00003333−3−3−3−30000i3−i3000000i3−i300000000
χ26222222-12-2-2-2-2-1-1222-11111-1-1-122-1-1-1-2-21111-211-2-1-1−2i2i11ii−i−i−2i−2iiiii2i2i−i−i−i−i0000−3−3−3−333330000−i3i3000000−i3i300000000
χ272222-2-22222-2-222222222222-2-2-2-22222-2-2-222222-2-2-200-2-2000000000000000022-2-222-2-222-2-20000000000000000000000
χ282222-2-22222-2-222222222222-2-2-2-22222-2-2-222222-2-2-200-2-20000000000000000-2-222-2-222-2-2220000000000000000000000
χ292222-2-222-2-222222222-2-2-2-22-2-2-2-2222-2222-2-2-2-2-22-2-200220000000000000000000000000000200-222000000-2-200000000
χ302222-2-222-2-222222222-2-2-2-22-2-2-2-2222-2222-2-2-2-2-22-2-200220000000000000000000000000000-2002-2-20000002200000000
χ312222-2-2-1222-2-2-1-1222-1-1-1-1-1-111-2-2-1-1-12-211-1-12-1-1-2110011−i3i3−i3i300−i3−i3i3i300−i3−i3i3i322-2-2-1-111-1-1110000−i3i3000000i3−i300000000
χ322222-2-2-1222-2-2-1-1222-1-1-1-1-1-111-2-2-1-1-12-211-1-12-1-1-2110011−i3i3−i3i300−i3−i3i3i300−i3−i3i3i3-2-22211-1-111-1-10000i3−i3000000−i3i300000000
χ332222-2-2-1222-2-2-1-1222-1-1-1-1-1-111-2-2-1-1-12-211-1-12-1-1-2110011i3−i3i3−i300i3i3−i3−i300i3i3−i3−i322-2-2-1-111-1-1110000i3−i3000000−i3i300000000
χ342222-2-2-1222-2-2-1-1222-1-1-1-1-1-111-2-2-1-1-12-211-1-12-1-1-2110011i3−i3i3−i300i3i3−i3−i300i3i3−i3−i3-2-22211-1-111-1-10000−i3i3000000i3−i300000000
χ352222-2-2-12-2-222-1-1222-11111-111-2-2-1-1-1-22-1-111-21121100-1-13−3−330033−3−300−3−333000033−3−3−3−333200-2-1-10000001100000000
χ362222-2-2-12-2-222-1-1222-11111-111-2-2-1-1-1-22-1-111-21121100-1-13−3−330033−3−300−3−3330000−3−33333−3−3-200211000000-1-100000000
χ372222-2-2-12-2-222-1-1222-11111-111-2-2-1-1-1-22-1-111-21121100-1-1−333−300−3−3330033−3−3000033−3−3−3−333-200211000000-1-100000000
χ382222-2-2-12-2-222-1-1222-11111-111-2-2-1-1-1-22-1-111-21121100-1-1−333−300−3−3330033−3−30000−3−33333−3−3200-2-1-10000001100000000
χ392-2-222-2222-22-2-2-2-2-22222-2-222-22-2-2-22-2-22-2-2-222222-2002-2000000000000000000000000000000000000002-2002-22-20000
χ402-2-222-2222-22-2-2-2-2-22222-2-222-22-2-2-22-2-22-2-2-222222-2002-200000000000000000000000000000000000000-2200-22-220000
χ412-2-222-222-22-22-2-2-2-222-2-22222-22-2-2-2222-2222-2-2-2-22-200-22000000000000000000000000000002-20002-22-2000000000000
χ422-2-222-222-22-22-2-2-2-222-2-22222-22-2-2-2222-2222-2-2-2-22-200-2200000000000000000000000000000-22000-22-22000000000000
χ432-2-222-22-12-22-2-2-211-1222-2-2-12-2-1111-1112-211-1-1-1-1-1100-110000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000000000−i3i3i3−i32-200-11-110000
χ442-2-222-22-12-22-2-2-211-1222-2-2-12-2-1111-1112-211-1-1-1-1-1100-110000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000000000i3−i3−i3i3-22001-11-10000
χ452-2-222-22-12-22-2-2-211-1222-2-2-12-2-1111-1112-211-1-1-1-1-1100-110000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000000000−i3i3i3−i3-22001-11-10000
χ462-2-222-22-12-22-2-2-211-1222-2-2-12-2-1111-1112-211-1-1-1-1-1100-110000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000000000i3−i3−i3i32-200-11-110000
χ472-2-222-22-1-22-22-2-211-12-2-222-12-2-1111-1-1-1-22-1-11111-11001-100003−33−33−3−33−33−3300000000000002-2000-11-1100003−3−330000
χ482-2-222-22-1-22-22-2-211-12-2-222-12-2-1111-1-1-1-22-1-11111-11001-100003−33−33−3−33−33−330000000000000-220001-11-10000−333−30000
χ492-2-222-22-1-22-22-2-211-12-2-222-12-2-1111-1-1-1-22-1-11111-11001-10000−33−33−333−33−33−300000000000002-2000-11-110000−333−30000
χ502-2-222-22-1-22-22-2-211-12-2-222-12-2-1111-1-1-1-22-1-11111-11001-10000−33−33−333−33−33−30000000000000-220001-11-100003−3−330000
χ512-2-22-22222-2-22-2-2-2-22222-2-22-22-22-2-22-22-22-2-2222-2-2200-220000000000000000000000000000000000000000000000002-2
χ522-2-22-22222-2-22-2-2-2-22222-2-22-22-22-2-22-22-22-2-2222-2-2200-22000000000000000000000000000000000000000000000000-22
χ532-2-22-2222-222-2-2-2-2-222-2-2222-22-22-2-222-22-222-2-2-22-22002-200000000000000000000000000000000000000000000002-200
χ542-2-22-2222-222-2-2-2-2-222-2-2222-22-22-2-222-22-222-2-2-22-22002-20000000000000000000000000000000000000000000000-2200
χ55444444-2-24444-2-2-2-2-2-2-2-2-2-21-2-2-2-2111-2-2-2-211-211-2114411-2-2-2-2-2-21111-2-211110000000000000000000000000000000000
χ56444444-2-24444-2-2-2-2-2-2-2-2-2-21-2-2-2-2111-2-2-2-211-211-211-4-411222222-1-1-1-122-1-1-1-10000000000000000000000000000000000
χ57444444-2-2-4-4-4-4-2-2-2-2-2-222221-2-2-2-21112222-1-12-1-12114i−4i-1-1−2i−2i2i2i−2i−2iiiii2i2i−i−i−i−i0000000000000000000000000000000000
χ58444444-2-2-4-4-4-4-2-2-2-2-2-222221-2-2-2-21112222-1-12-1-1211−4i4i-1-12i2i−2i−2i2i2i−i−i−i−i−2i−2iiiii0000000000000000000000000000000000
χ594444-4-44-244-4-444-2-2-244444-2-4-422-2-2-2-22-4-4-2-2-2-2-2222002200000000000000000000000000000000000000000000000000
χ604444-4-44-2-4-44444-2-2-24-4-4-4-4-2-4-422-2-2-22-24422222-22200-2-200000000000000000000000000000000000000000000000000
χ614444-4-4-2-244-4-4-2-2-2-2-2-2-2-2-2-212222111-222211-2112-1-100-1-1−2i32i3−2i32i300i3i3−i3−i300i3i3−i3−i30000000000000000000000000000000000
χ624444-4-4-2-244-4-4-2-2-2-2-2-2-2-2-2-212222111-222211-2112-1-100-1-12i3−2i32i3−2i300−i3−i3i3i300−i3−i3i3i30000000000000000000000000000000000
χ634444-4-4-2-2-4-444-2-2-2-2-2-22222122221112-2-2-2-1-12-1-1-2-1-1001123−23−232300−3−3330033−3−30000000000000000000000000000000000
χ644444-4-4-2-2-4-444-2-2-2-2-2-22222122221112-2-2-2-1-12-1-1-2-1-10011−232323−230033−3−300−3−3330000000000000000000000000000000000
χ6544-4-4004400004-44-4-4-40000400004-4-40000000000000000000000000000000000−2i22i200−2i22i200−2i22i20000000000000000000000
χ6644-4-4004400004-44-4-4-40000400004-4-400000000000000000000000000000000002i2−2i2002i2−2i2002i2−2i20000000000000000000000
χ6744-4-400-240000-224-4-4223−2323−23-20000-222000023−23023−230000000000000000000000000−2i22i2002ζ5+2ζ7−2ζ5−2ζ7002ζ13+2ζ23−2ζ13−2ζ230000000000000000000000
χ6844-4-400-240000-224-4-4223−2323−23-20000-222000023−23023−2300000000000000000000000002i2−2i200−2ζ5−2ζ72ζ5+2ζ700−2ζ13−2ζ232ζ13+2ζ230000000000000000000000
χ6944-4-400-240000-224-4-42−2323−2323-20000-2220000−23230−23230000000000000000000000000−2i22i2002ζ13+2ζ23−2ζ13−2ζ23002ζ5+2ζ7−2ζ5−2ζ70000000000000000000000
χ7044-4-400-240000-224-4-42−2323−2323-20000-2220000−23230−232300000000000000000000000002i2−2i200−2ζ13−2ζ232ζ13+2ζ2300−2ζ5−2ζ72ζ5+2ζ70000000000000000000000
χ714-44-400440000-44-44-4-4000040000-44-400000000000000000000000000000000−2i22i200−2i22i200−2i22i2000000000000000000000000
χ724-44-400440000-44-44-4-4000040000-44-4000000000000000000000000000000002i2−2i2002i2−2i2002i2−2i2000000000000000000000000
χ734-44-400-2400002-2-44-4223−23−2323-200002-220000−2323023−2300000000000000000000000−2i22i2002ζ13+2ζ23−2ζ13−2ζ23002ζ5+2ζ7−2ζ5−2ζ7000000000000000000000000
χ744-44-400-2400002-2-44-4223−23−2323-200002-220000−2323023−23000000000000000000000002i2−2i200−2ζ13−2ζ232ζ13+2ζ2300−2ζ5−2ζ72ζ5+2ζ7000000000000000000000000
χ754-44-400-2400002-2-44-42−232323−23-200002-22000023−230−232300000000000000000000000−2i22i2002ζ5+2ζ7−2ζ5−2ζ7002ζ13+2ζ23−2ζ13−2ζ23000000000000000000000000
χ764-44-400-2400002-2-44-42−232323−23-200002-22000023−230−2323000000000000000000000002i2−2i200−2ζ5−2ζ72ζ5+2ζ700−2ζ13−2ζ232ζ13+2ζ23000000000000000000000000
χ774-4-444-4-244-44-422-4-44-2-2-222-2-224-422-2-4-4-22224-2-24-2200-2200000000000000000000000000000000000000000000000000
χ784-4-444-4-24-44-4422-4-44-222-2-2-2-224-422-2442-2-2-2-422-4-22002-200000000000000000000000000000000000000000000000000
χ794-4-444-4-2-24-44-42222-2-2-2-2221-22-22-1-1122-22-1-1-211-21-1001-10000−2i32i3i3−i3i3−i3−2i32i3i3−i3i3−i30000000000000000000000000000000000
χ804-4-444-4-2-24-44-42222-2-2-2-2221-22-22-1-1122-22-1-1-211-21-1001-100002i3−2i3−i3i3−i3i32i3−2i3−i3i3−i3i30000000000000000000000000000000000
χ814-4-444-4-2-2-44-442222-2-222-2-21-22-22-1-11-2-22-2112-1-121-100-11000023−23−33−33−23233−33−30000000000000000000000000000000000
χ824-4-444-4-2-2-44-442222-2-222-2-21-22-22-1-11-2-22-2112-1-121-100-110000−23233−33−323−23−33−330000000000000000000000000000000000
χ834-4-44-444-24-4-44-4-422-2444-4-4-2-442-222-22-2-4422-2-2-222-2002-200000000000000000000000000000000000000000000000000
χ844-4-44-444-2-444-4-4-422-24-4-444-2-442-222-2-224-4-2-2222-22-200-2200000000000000000000000000000000000000000000000000
χ854-4-44-44-244-4-4422-4-44-2-2-222-22-2-4422-2-442-2224-2-2-42-2002-200000000000000000000000000000000000000000000000000
χ864-4-44-44-24-444-422-4-44-222-2-2-22-2-4422-24-4-22-2-2-42242-200-2200000000000000000000000000000000000000000000000000
χ874-4-44-44-2-24-4-442222-2-2-2-22212-22-2-1-112-22-2-1-1-2112-1100-110000003-3-33003-3-330000000000000000000000000000000000
χ884-4-44-44-2-24-4-442222-2-2-2-22212-22-2-1-112-22-2-1-1-2112-1100-11000000-333-300-333-30000000000000000000000000000000000
χ894-4-44-44-2-2-444-42222-2-222-2-212-22-2-1-11-22-22112-1-1-2-11001-10000003i−3i−3i3i00−3i3i3i−3i0000000000000000000000000000000000
χ904-4-44-44-2-2-444-42222-2-222-2-212-22-2-1-11-22-22112-1-1-2-11001-1000000−3i3i3i−3i003i−3i−3i3i0000000000000000000000000000000000
χ9188-8-8008-400008-8-444-80000-40000-444000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-800-4-40000-44-444443−4343−43200002-2-20000−23230−2323000000000000000000000000000000000000000000000000000000000
χ9388-8-800-4-40000-44-4444−4343−4343200002-2-2000023−23023−23000000000000000000000000000000000000000000000000000000000
χ948-88-8008-40000-884-44-80000-400004-44000000000000000000000000000000000000000000000000000000000000000000
χ958-88-800-4-400004-44-44443−43−434320000-22-2000023−230−2323000000000000000000000000000000000000000000000000000000000
χ968-88-800-4-400004-44-444−434343−4320000-22-20000−2323023−23000000000000000000000000000000000000000000000000000000000

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