Finite Group Databasebeta

← Group #11787651

Character table — Group #11787651

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222222222222444444444444444444448888888888888888888888121212121212121224242424242424242424242424242424242424243636363636363636
order12442223344466121212123666666666121212121212121212126688121224242424242424242424242424242424224488882444666612121212121212122424242488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111
χ81111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-11111-1-1-1-1
χ911-1-11-1-11111-111-1-1-1-111-11-1-1-1-11-11-11-1-1-111111-11-11-111111111-1-1-1-1-1-1-1-11-11-1ii−i−i1-1i−i1-1111-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011-1-11-1-11111-111-1-1-1-111-11-1-1-1-11-11-11-1-1-111111-11-11-111111111-1-1-1-1-1-1-1-11-11-1−i−iii1-1−ii1-1111-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111-1-11-1-11111-111-1-1-1-111-11-1-1-1-11-11-11-1-1-111111-11-11-111111111-1-1-1-1-1-1-1-1-11-11ii−i−i-11i−i-11-1-1-1111ii−i−iii−i−i−i−iii−i−iii
χ1211-1-11-1-11111-111-1-1-1-111-11-1-1-1-11-11-11-1-1-111111-11-11-111111111-1-1-1-1-1-1-1-1-11-11−i−iii-11−ii-11-1-1-1111−i−iii−i−iiiii−i−iii−i−i
χ1311-1-11-1-11111-111-1-1-1-111-11-1-1-1-11-11-11-1-1-111111-1-111-1-1-1-1-1-1-1-1-1111111111-11-1ii−i−i-11−ii1-1-1-11-111−i−iiiii−i−iii−i−i−i−iii
χ1411-1-11-1-11111-111-1-1-1-111-11-1-1-1-11-11-11-1-1-111111-1-111-1-1-1-1-1-1-1-1-1111111111-11-1−i−iii-11i−i1-1-1-11-111ii−i−i−i−iii−i−iiiii−i−i
χ1511-1-11-1-11111-111-1-1-1-111-11-1-1-1-11-11-11-1-1-111111-1-111-1-1-1-1-1-1-1-1-111111111-11-11ii−i−i1-1−ii-1111-11-1-1−i−iiiii−i−i−i−iiiii−i−i
χ1611-1-11-1-11111-111-1-1-1-111-11-1-1-1-11-11-11-1-1-111111-1-111-1-1-1-1-1-1-1-1-111111111-11-11−i−iii1-1i−i-1111-11-1-1ii−i−i−i−iiiii−i−i−i−iii
χ1722222222-12222-1-1-122-122-1-1-1-1-1-1222-1-1-1-12-1-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-1-1222200002200-1-1-1-1-1-1-1-10000000000000000
χ1822222222-12222-1-1-122-122-1-1-1-1-1-1222-1-1-1-12-1-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-20000-2-200111111110000000000000000
χ1922222222-12222-1-1-122-122-1-1-1-1-1-1222-1-1-1-12-1-1-1-1-1-2-2-1-1-2-2111111-2-211111122220000-2-200-1-111-1-1110000000000000000
χ2022222222-12222-1-1-122-122-1-1-1-1-1-1222-1-1-1-12-1-1-1-1-1-2-2-1-1-2-2111111-2-2111111-2-2-2-20000220011-1-111-1-10000000000000000
χ212222222-12222-1222-1-1-1-1-1222-1-1-1-1-1-122-1-1-12-1-1-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-100002222002200000000-1-1-1-1-1-1-1-100000000
χ222222222-12222-1222-1-1-1-1-1222-1-1-1-1-1-122-1-1-12-1-1-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-10000-2-2-2-200-2-2000000001111111100000000
χ232222222-12222-1222-1-1-1-1-1222-1-1-1-1-1-122-1-1-12-1-1-1-1-2-2-1-111-2-2111111-2-211110000222200-2-2000000001111-1-1-1-100000000
χ242222222-12222-1222-1-1-1-1-1222-1-1-1-1-1-122-1-1-12-1-1-1-1-2-2-1-111-2-2111111-2-211110000-2-2-2-2002200000000-1-1-1-1111100000000
χ2522222-2-222-2-2222222222-22-2-2-2-22-2-22-2222-2-2-2-22-200-22000000000000000000002-22-200000000000000002-22-200000000
χ2622222-2-222-2-2222222222-22-2-2-2-22-2-22-2222-2-2-2-22-200-2200000000000000000000-22-220000000000000000-22-2200000000
χ2722222-2-2-12-2-22-1222-1-1-1-112-2-211-111-1-22-1-11-211-11001-13−30033−3−33−30033−3−300002-22-20000000000003−33−3-11-1100000000
χ2822222-2-2-12-2-22-1222-1-1-1-112-2-211-111-1-22-1-11-211-11001-13−30033−3−33−30033−3−30000-22-22000000000000−33−331-11-100000000
χ2922222-2-2-12-2-22-1222-1-1-1-112-2-211-111-1-22-1-11-211-11001-1−3300−3−333−3300−3−33300002-22-2000000000000−33−33-11-1100000000
χ3022222-2-2-12-2-22-1222-1-1-1-112-2-211-111-1-22-1-11-211-11001-1−3300−3−333−3300−3−3330000-22-220000000000003−33−31-11-100000000
χ312222-22-222-22-22222222-22-22-2222-2-2-2-2-2222222-2-200-2-200000000000000002-2-22000000002-200-22000000000000000000
χ322222-22-222-22-22222222-22-22-2222-2-2-2-2-2222222-2-200-2-20000000000000000-222-200000000-22002-2000000000000000000
χ332222-22-22-1-22-22-1-1-122-1-221-11-1-1-1-2-2-211-1-12-1-1-111001100−i3i3−i3i3−i3i300−i3i3−i3i3−i3i32-2-2200000000-11−i3i31-1−i3i30000000000000000
χ342222-22-22-1-22-22-1-1-122-1-221-11-1-1-1-2-2-211-1-12-1-1-111001100−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3-222-2000000001-1i3−i3-11i3−i30000000000000000
χ352222-22-22-1-22-22-1-1-122-1-221-11-1-1-1-2-2-211-1-12-1-1-111001100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i32-2-2200000000-11i3−i31-1i3−i30000000000000000
χ362222-22-22-1-22-22-1-1-122-1-221-11-1-1-1-2-2-211-1-12-1-1-111001100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3-222-2000000001-1−i3i3-11−i3i30000000000000000
χ372222-2-22222-2-22222222-2-2-2-22-2-2222-22-222-2-2-2-2-22002-2000000000000000000000000000000000000000000002-22-20000
χ382222-2-22222-2-22222222-2-2-2-22-2-2222-22-222-2-2-2-2-22002-200000000000000000000000000000000000000000000-22-220000
χ3922-2-222222-2-2-222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-22200-2-2000000000000000000002i−2i−2i2i00000000000000002i−2i−2i2i00000000
χ4022-2-222222-2-2-222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-22200-2-200000000000000000000−2i2i2i−2i0000000000000000−2i2i2i−2i00000000
χ4122-2-2222-12-2-2-2-12-2-211-1-1-1222-1-1-1-111-2-2111-211-1-100113−30033−3−3−3300−3−33300002i−2i−2i2i000000000000i3−i3−i3i3−iii−i00000000
χ4222-2-2222-12-2-2-2-12-2-211-1-1-1222-1-1-1-111-2-2111-211-1-100113−30033−3−3−3300−3−3330000−2i2i2i−2i000000000000−i3i3i3−i3i−i−ii00000000
χ4322-2-2222-12-2-2-2-12-2-211-1-1-1222-1-1-1-111-2-2111-211-1-10011−3300−3−3333−30033−3−300002i−2i−2i2i000000000000−i3i3i3−i3−iii−i00000000
χ4422-2-2222-12-2-2-2-12-2-211-1-1-1222-1-1-1-111-2-2111-211-1-10011−3300−3−3333−30033−3−30000−2i2i2i−2i000000000000i3−i3−i3i3i−i−ii00000000
χ4522-2-22-2-22-122-22-111-2-2-12-2-11111-1-22-2-11112-1-1-1-112-2-1122-1-1-1-1-1-1-2-21111112-22-200002-200-11-1-1-11110000000000000000
χ4622-2-22-2-22-122-22-111-2-2-12-2-11111-1-22-2-11112-1-1-1-112-2-1122-1-1-1-1-1-1-2-2111111-22-220000-22001-1111-1-1-10000000000000000
χ4722-2-22-2-22-122-22-111-2-2-12-2-11111-1-22-2-11112-1-1-1-11-22-11-2-211111122-1-1-1-1-1-12-22-20000-2200-1111-11-1-10000000000000000
χ4822-2-22-2-22-122-22-111-2-2-12-2-11111-1-22-2-11112-1-1-1-11-22-11-2-211111122-1-1-1-1-1-1-22-2200002-2001-1-1-11-1110000000000000000
χ4922-2-22-2-2-1222-2-12-2-211-1-112-2-211-11-112-211-12-1-1-112-2-11-1-122-1-1-1-111-2-2111100002i2i−2i−2i002i−2i00000000−i−iii−i−iii00000000
χ5022-2-22-2-2-1222-2-12-2-211-1-112-2-211-11-112-211-12-1-1-112-2-11-1-122-1-1-1-111-2-211110000−2i−2i2i2i00−2i2i00000000ii−i−iii−i−i00000000
χ5122-2-22-2-2-1222-2-12-2-211-1-112-2-211-11-112-211-12-1-1-11-22-1111-2-21111-1-122-1-1-1-100002i2i−2i−2i00−2i2i00000000ii−i−i−i−iii00000000
χ5222-2-22-2-2-1222-2-12-2-211-1-112-2-211-11-112-211-12-1-1-11-22-1111-2-21111-1-122-1-1-1-10000−2i−2i2i2i002i−2i00000000−i−iiiii−i−i00000000
χ5322-2-2-22-2222-2222-2-2-2-22-22-22-2222-22222-2-2-2-2-2-2-2-20022000000000000000000000000000000000000000000002i−2i−2i2i0000
χ5422-2-2-22-2222-2222-2-2-2-22-22-22-2222-22222-2-2-2-2-2-2-2-2002200000000000000000000000000000000000000000000−2i2i2i−2i0000
χ5522-2-2-2-2222-22222-2-2-2-22-2-2-2-22-2-222-22-22-2-22222-2200-22000000000000000022-2-2000000002200-2-2000000000000000000
χ5622-2-2-2-2222-22222-2-2-2-22-2-2-2-22-2-222-22-22-2-22222-2200-220000000000000000-2-22200000000-2-20022000000000000000000
χ5722-2-2-2-222-1-2222-111-2-2-1-2-211-111-12-221-1112-1-1-11-1001-100−i3i3−i3i3−i3i300i3−i3i3−i3i3−i322-2-200000000-1-1−i3i311i3−i30000000000000000
χ5822-2-2-2-222-1-2222-111-2-2-1-2-211-111-12-221-1112-1-1-11-1001-100−i3i3−i3i3−i3i300i3−i3i3−i3i3−i3-2-2220000000011i3−i3-1-1−i3i30000000000000000
χ5922-2-2-2-222-1-2222-111-2-2-1-2-211-111-12-221-1112-1-1-11-1001-100i3−i3i3−i3i3−i300−i3i3−i3i3−i3i322-2-200000000-1-1i3−i311−i3i30000000000000000
χ6022-2-2-2-222-1-2222-111-2-2-1-2-211-111-12-221-1112-1-1-11-1001-100i3−i3i3−i3i3−i300−i3i3−i3i3−i3i3-2-2220000000011−i3i3-1-1i3−i30000000000000000
χ614444444-2-2444-2-2-2-2-2-21-2-2-2-2-2111-2-2-2-2-211-2-211114411-2-2-2-21111-2-2-2-21111000000000000000000000000000000000000
χ624444444-2-2444-2-2-2-2-2-21-2-2-2-2-2111-2-2-2-2-211-2-21111-4-4112222-1-1-1-12222-1-1-1-1000000000000000000000000000000000000
χ6344444-4-44-2-4-444-2-2-244-24-4-22222-2-4-442-2-2-2-4222-22002-20000000000000000000000000000000000000000000000000000
χ6444444-4-4-2-2-4-44-2-2-2-2-2-21-22-222-1-1122-22-21122-1-11-100-1123−2300−3−33323−2300−3−333000000000000000000000000000000000000
χ6544444-4-4-2-2-4-44-2-2-2-2-2-21-22-222-1-1122-22-21122-1-11-100-11−23230033−3−3−23230033−3−3000000000000000000000000000000000000
χ664444-44-4-24-44-4-2444-2-2-22-2-44-4-2-2-2222-4-4-2-2-24-2-22200220000000000000000000000000000000000000000000000000000
χ674444-44-4-2-2-44-4-2-2-2-2-2-212-22-221112222211-2-211-1-100-1-100−2i32i3i3−i3i3−i300−2i32i3i3−i3i3−i3000000000000000000000000000000000000
χ684444-44-4-2-2-44-4-2-2-2-2-2-212-22-221112222211-2-211-1-100-1-1002i3−2i3−i3i3−i3i3002i3−2i3−i3i3−i3i3000000000000000000000000000000000000
χ694444-4-444-24-4-44-2-2-244-2-4-422-222-244-4-22-2-2-42222-200-220000000000000000000000000000000000000000000000000000
χ704444-4-44-244-4-4-2444-2-2-222-4-4422-2-2-224-4-2-22-4222-200-220000000000000000000000000000000000000000000000000000
χ714444-4-44-2-24-4-4-2-2-2-2-2-212222-2-1-11-2-22-221122-1-1-11001-100003i−3i−3i3i00003i−3i−3i3i000000000000000000000000000000000000
χ724444-4-44-2-24-4-4-2-2-2-2-2-212222-2-1-11-2-22-221122-1-1-11001-10000−3i3i3i−3i0000−3i3i3i−3i000000000000000000000000000000000000
χ7344-4-44444-2-4-4-44-222-4-4-244-2-2-2-2-2-24-4-42222-4222-2-200220000000000000000000000000000000000000000000000000000
χ7444-4-4444-2-2-4-4-4-2-222221-2-2-2-2-2111-22222-1-122-1-11100-1-123−2300−3−333−23230033−3−3000000000000000000000000000000000000
χ7544-4-4444-2-2-4-4-4-2-222221-2-2-2-2-2111-22222-1-122-1-11100-1-1−23230033−3−323−2300−3−333000000000000000000000000000000000000
χ7644-4-44-4-4-2-244-4-2-222221-22-222-1-112-22-22-1-1-2-2111-14-41-1-2-2-2-211112222-1-1-1-1000000000000000000000000000000000000
χ7744-4-44-4-4-2-244-4-2-222221-22-222-1-112-22-22-1-1-2-2111-1-441-12222-1-1-1-1-2-2-2-21111000000000000000000000000000000000000
χ7844-4-4-44-44-24-444-222-4-4-2-442-22-2-2-2-444-2-222-42222200-2-20000000000000000000000000000000000000000000000000000
χ7944-4-4-44-4-244-44-24-4-422-22-2-44-4-2-2-22-2-244222-4222200-2-20000000000000000000000000000000000000000000000000000
χ8044-4-4-44-4-2-24-44-2-2222212-22-221112-2-2-2-2-1-122-1-1-1-1001100003i−3i−3i3i0000−3i3i3i−3i000000000000000000000000000000000000
χ8144-4-4-44-4-2-24-44-2-2222212-22-221112-2-2-2-2-1-122-1-1-1-100110000−3i3i3i−3i00003i−3i−3i3i000000000000000000000000000000000000
χ8244-4-4-4-44-24-444-24-4-422-222-4-4422-2-22-2-4422-24-2-22-2002-20000000000000000000000000000000000000000000000000000
χ8344-4-4-4-44-2-2-444-2-2222212222-2-1-11-22-22-2-1-1-2-211-1100-1100−2i32i3i3−i3i3−i3002i3−2i3−i3i3−i3i3000000000000000000000000000000000000
χ8444-4-4-4-44-2-2-444-2-2222212222-2-1-11-22-22-2-1-1-2-211-1100-11002i3−2i3−i3i3−i3i300−2i32i3i3−i3i3−i3000000000000000000000000000000000000
χ854-44i−4i00044000-4-44i−4i4i−4i40000000-4000004i−4i00000000000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13
χ864-44i−4i00044000-4-44i−4i4i−4i40000000-4000004i−4i0000000000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13
χ874-4−4i4i00044000-4-4−4i4i−4i4i40000000-400000−4i4i0000000000000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23
χ884-4−4i4i00044000-4-4−4i4i−4i4i40000000-400000−4i4i00000000000000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23
χ898-88i−8i0008-4000-84−4i4i8i−8i-40000000400000−4i4i00000000000000000000000000000000000000000000000000000000000000
χ908-88i−8i000-480004-88i−8i−4i4i-40000000400000−4i4i00000000000000000000000000000000000000000000000000000000000000
χ918-88i−8i000-4-400044−4i4i−4i4i2000006-6-2000002i−2i006i−6i0000000000000000000000000000000000000000000000000000000000
χ928-88i−8i000-4-400044−4i4i−4i4i200000-66-2000002i−2i00−6i6i0000000000000000000000000000000000000000000000000000000000
χ938-8−8i8i0008-4000-844i−4i−8i8i-400000004000004i−4i00000000000000000000000000000000000000000000000000000000000000
χ948-8−8i8i000-480004-8−8i8i4i−4i-400000004000004i−4i00000000000000000000000000000000000000000000000000000000000000
χ958-8−8i8i000-4-4000444i−4i4i−4i2000006-6-200000−2i2i00−6i6i0000000000000000000000000000000000000000000000000000000000
χ968-8−8i8i000-4-4000444i−4i4i−4i200000-66-200000−2i2i006i−6i0000000000000000000000000000000000000000000000000000000000

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