Finite Group Databasebeta

← Group #11787634

Character table — Group #11787634

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222222222222444444444444444444448888888888888888888888121212121212121224242424242424242424242424242424242424243636363636363636
order1244222334446612121212366666666612121212121212121212446612121212121212121212121212121212121288888888246688121224242424242424242424242422448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ511111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911-1-11-1-11111-111-1-1-1-111-11-1-1-11-1-11-111-111-1-11i−i1-11-1iiiiiiii−i−i−i−i−i−i−i−iii−i−iii−i−i1-1111-1-1-1ii−i−iii−i−i11-1-11-11-1ii−i−i
χ1011-1-11-1-11111-111-1-1-1-111-11-1-1-11-1-11-111-111-1-11i−i1-11-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i−i−iii1-111-11-1-1ii−i−i−i−iii-1-111-11-11−i−iii
χ1111-1-11-1-11111-111-1-1-1-111-11-1-1-11-1-11-111-111-1-11i−i1-11-1iiiiiiii−i−i−i−i−i−i−i−i−i−iiiii−i−i-11-1-11-111−i−iiiii−i−i11-1-1-11-11−i−iii
χ1211-1-11-1-11111-111-1-1-1-111-11-1-1-11-1-11-111-111-1-11i−i1-11-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−iii-11-1-1-1111−i−iii−i−iii-1-1111-11-1ii−i−i
χ1311-1-11-1-11111-111-1-1-1-111-11-1-1-11-1-11-111-111-1-11−ii1-11-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−iii−i−i-11-1-1-1111ii−i−iii−i−i-1-1111-11-1−i−iii
χ1411-1-11-1-11111-111-1-1-1-111-11-1-1-11-1-11-111-111-1-11−ii1-11-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i−i−iii-11-1-11-111ii−i−i−i−iii11-1-1-11-11ii−i−i
χ1511-1-11-1-11111-111-1-1-1-111-11-1-1-11-1-11-111-111-1-11−ii1-11-1−i−i−i−i−i−i−i−iiiiiiiii−i−iiiii−i−i1-111-11-1-1−i−iiiii−i−i-1-111-11-11ii−i−i
χ1611-1-11-1-11111-111-1-1-1-111-11-1-1-11-1-11-111-111-1-11−ii1-11-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−iii1-1111-1-1-1−i−iii−i−iii11-1-11-11-1−i−iii
χ1722222222-12222-122-1-1-122-1-12-1-1-1-122-1-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12222000022-1-100-1-1-1-1-1-10000000000000000
χ1822222222-12222-122-1-1-122-1-12-1-1-1-122-1-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-20000-2-211001111110000000000000000
χ1922222222-12222-122-1-1-122-1-12-1-1-1-122-1-1-1-1-1-1-12-2-2-1-1-1-1-2-2111111-2-211111122220000-2-2110011-1-1-1-10000000000000000
χ2022222222-12222-122-1-1-122-1-12-1-1-1-122-1-1-1-1-1-1-12-2-2-1-1-1-1-2-2111111-2-2111111-2-2-2-2000022-1-100-1-111110000000000000000
χ212222222-12222-12-1-122-1-1-122-12-1-1-1-1-1222-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100002222000022000000-1-1-1-1-1-1-1-100000000
χ222222222-12222-12-1-122-1-1-122-12-1-1-1-1-1222-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-10000-2-2-2-20000-2-20000001111111100000000
χ232222222-12222-12-1-122-1-1-122-12-1-1-1-1-1222-1-1-1-1-1-2-2-1-1-1-111-2-2111111-2-21111000022220000-2-2000000-1-1-1-1111100000000
χ242222222-12222-12-1-122-1-1-122-12-1-1-1-1-1222-1-1-1-1-1-2-2-1-1-1-111-2-2111111-2-211110000-2-2-2-20000220000001111-1-1-1-100000000
χ2522222-2-222-2-2222222222-22-2-2-22-2-2-22-2-22-2-222-2002-2-22000000000000000000002-22-20000000000002-22-2000000000000
χ2622222-2-222-2-2222222222-22-2-2-22-2-2-22-2-22-2-222-2002-2-2200000000000000000000-22-22000000000000-22-22000000000000
χ2722222-2-2-12-2-22-12-1-122-1-112-21-2-1111-1-2-2211-1-1100-111-13−30033−3−33−30033−3−300002-22-2000000000000-11-113−33−300000000
χ2822222-2-2-12-2-22-12-1-122-1-112-21-2-1111-1-2-2211-1-1100-111-13−30033−3−33−30033−3−30000-22-220000000000001-11-1−33−3300000000
χ2922222-2-2-12-2-22-12-1-122-1-112-21-2-1111-1-2-2211-1-1100-111-1−3300−3−333−3300−3−33300002-22-2000000000000-11-11−33−3300000000
χ3022222-2-2-12-2-22-12-1-122-1-112-21-2-1111-1-2-2211-1-1100-111-1−3300−3−333−3300−3−3330000-22-220000000000001-11-13−33−300000000
χ312222-22-222-22-22222222-22-22-2-22-2-2-2-22-2-2-2-222200-222-2000000000000000000000000000000000000000000002-2-220000
χ322222-22-222-22-22222222-22-22-2-22-2-2-2-22-2-2-2-222200-222-200000000000000000000000000000000000000000000-222-20000
χ332222-2-22222-2-22222222-2-2-2-2222222-2-22-22222-200-2-2-2-200000000000000002-22-20000000000002-22-20000000000000000
χ342222-2-22222-2-22222222-2-2-2-2222222-2-22-22222-200-2-2-2-20000000000000000-22-22000000000000-22-220000000000000000
χ352222-2-222-12-2-22-122-1-1-1-2-2112-1-1-1-12-21-11-1-1-1-1-200111100−i3i3−i3i3−i3i300−i3i3−i3i3−i3i32-22-2000000−i3i300−i3i3-11-110000000000000000
χ362222-2-222-12-2-22-122-1-1-1-2-2112-1-1-1-12-21-11-1-1-1-1-200111100−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3-22-22000000i3−i300i3−i31-11-10000000000000000
χ372222-2-222-12-2-22-122-1-1-1-2-2112-1-1-1-12-21-11-1-1-1-1-200111100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i32-22-2000000i3−i300i3−i3-11-110000000000000000
χ382222-2-222-12-2-22-122-1-1-1-2-2112-1-1-1-12-21-11-1-1-1-1-200111100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3-22-22000000−i3i300−i3i31-11-10000000000000000
χ3922-2-222222-2-2-222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-20022-2-2000000000000000000002i−2i−2i2i0000000000002i−2i−2i2i000000000000
χ4022-2-222222-2-2-222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-20022-2-200000000000000000000−2i2i2i−2i000000000000−2i2i2i−2i000000000000
χ4122-2-2222-12-2-2-2-1211-2-2-1-1-122-12-1-1-111-2-2-21111100-1-111−i3i300−i3−i3i3i3i3−i300i3i3−i3−i300002i−2i−2i2i000000000000−iii−i−333−300000000
χ4222-2-2222-12-2-2-2-1211-2-2-1-1-122-12-1-1-111-2-2-21111100-1-111−i3i300−i3−i3i3i3i3−i300i3i3−i3−i30000−2i2i2i−2i000000000000i−i−ii3−3−3300000000
χ4322-2-2222-12-2-2-2-1211-2-2-1-1-122-12-1-1-111-2-2-21111100-1-111i3−i300i3i3−i3−i3−i3i300−i3−i3i3i300002i−2i−2i2i000000000000−iii−i3−3−3300000000
χ4422-2-2222-12-2-2-2-1211-2-2-1-1-122-12-1-1-111-2-2-21111100-1-111i3−i300i3i3−i3−i3−i3i300−i3−i3i3i30000−2i2i2i−2i000000000000i−i−ii−333−300000000
χ4522-2-22-2-22-122-22-1-2-211-12-2-11-21-1112-2-1-11-1-11122i−2i-11-112i2i−i−i−i−i−i−i−2i−2iiiiiii2i2i−2i−2i00002-2-1-10011−i−iii0000000000000000
χ4622-2-22-2-22-122-22-1-2-211-12-2-11-21-1112-2-1-11-1-11122i−2i-11-112i2i−i−i−i−i−i−i−2i−2iiiiiii−2i−2i2i2i0000-221100-1-1ii−i−i0000000000000000
χ4722-2-22-2-22-122-22-1-2-211-12-2-11-21-1112-2-1-11-1-1112−2i2i-11-11−2i−2iiiiiii2i2i−i−i−i−i−i−i2i2i−2i−2i0000-221100-1-1−i−iii0000000000000000
χ4822-2-22-2-22-122-22-1-2-211-12-2-11-21-1112-2-1-11-1-1112−2i2i-11-11−2i−2iiiiiii2i2i−i−i−i−i−i−i−2i−2i2i2i00002-2-1-10011ii−i−i0000000000000000
χ4922-2-22-2-2-1222-2-1211-2-2-1-112-21-2-111-1122-2-1-111-12i−2i-11-11−i−i2i2i−i−i−i−iii−2i−2iiiii00002i2i−2i−2i00002-2000000−i−iii-1-11100000000
χ5022-2-22-2-2-1222-2-1211-2-2-1-112-21-2-111-1122-2-1-111-12i−2i-11-11−i−i2i2i−i−i−i−iii−2i−2iiiii0000−2i−2i2i2i0000-22000000ii−i−i11-1-100000000
χ5122-2-22-2-2-1222-2-1211-2-2-1-112-21-2-111-1122-2-1-111-1−2i2i-11-11ii−2i−2iiiii−i−i2i2i−i−i−i−i00002i2i−2i−2i0000-22000000−i−iii11-1-100000000
χ5222-2-22-2-2-1222-2-1211-2-2-1-112-21-2-111-1122-2-1-111-1−2i2i-11-11ii−2i−2iiiii−i−i2i2i−i−i−i−i0000−2i−2i2i2i00002-2000000ii−i−i-1-11100000000
χ5322-2-2-22-2222-2222-2-2-2-22-22-22-2-22-2-222-22222-2-2-200-22-2200000000000000002i−2i−2i2i0000000000002i−2i−2i2i0000000000000000
χ5422-2-2-22-2222-2222-2-2-2-22-22-22-2-22-2-222-22222-2-2-200-22-220000000000000000−2i2i2i−2i000000000000−2i2i2i−2i0000000000000000
χ5522-2-2-22-22-12-222-1-2-211-1-221-1-21-111221-1-1-1-111-2001-11-1003−33−33−300−33−33−332i−2i−2i2i000000−i3i300i3−i3−iii−i0000000000000000
χ5622-2-2-22-22-12-222-1-2-211-1-221-1-21-111221-1-1-1-111-2001-11-1003−33−33−300−33−33−33−2i2i2i−2i000000i3−i300−i3i3i−i−ii0000000000000000
χ5722-2-2-22-22-12-222-1-2-211-1-221-1-21-111221-1-1-1-111-2001-11-100−33−33−33003−33−33−32i−2i−2i2i000000i3−i300−i3i3−iii−i0000000000000000
χ5822-2-2-22-22-12-222-1-2-211-1-221-1-21-111221-1-1-1-111-2001-11-100−33−33−33003−33−33−3−2i2i2i−2i000000−i3i300i3−i3i−i−ii0000000000000000
χ5922-2-2-2-2222-22222-2-2-2-22-2-2-2-222222-222-22-2-2-2-2200-2-2220000000000000000000000000000000000000000000022-2-20000
χ6022-2-2-2-2222-22222-2-2-2-22-2-2-2-222222-222-22-2-2-2-2200-2-22200000000000000000000000000000000000000000000-2-2220000
χ614444444-2-2444-2-2-2-2-2-21-2-2-2-2-2-2111-2-2-2-2-21111-2441111-2-2-2-21111-2-2-2-21111000000000000000000000000000000000000
χ624444444-2-2444-2-2-2-2-2-21-2-2-2-2-2-2111-2-2-2-2-21111-2-4-411112222-1-1-1-12222-1-1-1-1000000000000000000000000000000000000
χ6344444-4-44-2-4-444-244-2-2-24-4-22-42-222-4422-222-2-2-400-222-20000000000000000000000000000000000000000000000000000
χ6444444-4-4-2-2-4-44-2-2-2-2-2-21-22-22221-1-12-222-2-1-1112001-1-1123−2300−3−33323−2300−3−333000000000000000000000000000000000000
χ6544444-4-4-2-2-4-44-2-2-2-2-2-21-22-22221-1-12-222-2-1-1112001-1-11−23230033−3−3−23230033−3−3000000000000000000000000000000000000
χ664444-44-44-2-44-44-244-2-2-2-442-2-42-222-4-4-22222-2-24002-2-220000000000000000000000000000000000000000000000000000
χ674444-44-4-24-44-4-24-2-244-22-2-442-4-222224-4-422-2-2-2002-2-220000000000000000000000000000000000000000000000000000
χ684444-44-4-2-2-44-4-2-2-2-2-2-212-22-2221-1-122-222-1-111-200-111-100003i−3i−3i3i00003i−3i−3i3i000000000000000000000000000000000000
χ694444-44-4-2-2-44-4-2-2-2-2-2-212-22-2221-1-122-222-1-111-200-111-10000−3i3i3i−3i0000−3i3i3i−3i000000000000000000000000000000000000
χ704444-4-44-244-4-4-24-2-244-222-4-4-24-2-2-2-22-44-4-2-2-2-220022220000000000000000000000000000000000000000000000000000
χ714444-4-44-2-24-4-4-2-2-2-2-2-212222-2-2111-222-221111200-1-1-1-100−2i32i3i3−i3i3−i300−2i32i3i3−i3i3−i3000000000000000000000000000000000000
χ724444-4-44-2-24-4-4-2-2-2-2-2-212222-2-2111-222-221111200-1-1-1-1002i3−2i3−i3i3−i3i3002i3−2i3−i3i3−i3i3000000000000000000000000000000000000
χ7344-4-44444-2-4-4-44-2-4-422-244-2-24-2-2-2-2-4-42222222-400-2-2220000000000000000000000000000000000000000000000000000
χ7444-4-4444-2-2-4-4-4-2-222221-2-2-2-2-2-211122222-1-1-1-120011-1-1−2i32i300i3i3−i3−i32i3−2i300−i3−i3i3i3000000000000000000000000000000000000
χ7544-4-4444-2-2-4-4-4-2-222221-2-2-2-2-2-211122222-1-1-1-120011-1-12i3−2i300−i3−i3i3i3−2i32i300i3i3−i3−i3000000000000000000000000000000000000
χ7644-4-44-4-4-2-244-4-2-222221-22-22221-1-1-22-2-2211-1-1-24i−4i1-11-1−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i000000000000000000000000000000000000
χ7744-4-44-4-4-2-244-4-2-222221-22-22221-1-1-22-2-2211-1-1-2−4i4i1-11-12i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii000000000000000000000000000000000000
χ7844-4-4-44-4-244-44-2422-4-4-22-2-442-4-222-2-2-444-2-2222002-22-20000000000000000000000000000000000000000000000000000
χ7944-4-4-44-4-2-24-44-2-2222212-22-2221-1-1-2-22-2-211-1-1200-11-110023−23−33−3300−23233−33−3000000000000000000000000000000000000
χ8044-4-4-44-4-2-24-44-2-2222212-22-2221-1-1-2-22-2-211-1-1200-11-1100−23233−33−30023−23−33−33000000000000000000000000000000000000
χ8144-4-4-4-444-2-4444-2-4-422-2-4-4224-2-2-2-2-44-22-2222240022-2-20000000000000000000000000000000000000000000000000000
χ8244-4-4-4-44-24-444-2422-4-4-222-4-4-24-2-2-22-24-442222-20022-2-20000000000000000000000000000000000000000000000000000
χ8344-4-4-4-44-2-2-444-2-2222212222-2-21112-2-22-2-1-1-1-1-200-1-11100003-3-330000-333-3000000000000000000000000000000000000
χ8444-4-4-4-44-2-2-444-2-2222212222-2-21112-2-22-2-1-1-1-1-200-1-1110000-333-300003-3-33000000000000000000000000000000000000
χ854-44i−4i00044000-4-44i−4i4i−4i4000000-40000000004i−4i00000000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13
χ864-44i−4i00044000-4-44i−4i4i−4i4000000-40000000004i−4i0000000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13
χ874-4−4i4i00044000-4-4−4i4i−4i4i4000000-4000000000−4i4i0000000000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23
χ884-4−4i4i00044000-4-4−4i4i−4i4i4000000-4000000000−4i4i00000000000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23
χ898-88i−8i0008-4000-848i−8i−4i4i-40000004000000000−4i4i00000000000000000000000000000000000000000000000000000000000
χ908-88i−8i000-480004-8−4i4i8i−8i-40000004000000000−4i4i00000000000000000000000000000000000000000000000000000000000
χ918-88i−8i000-4-400044−4i4i−4i4i2000000-26-6000006i−6i2i−2i00000000000000000000000000000000000000000000000000000000000
χ928-88i−8i000-4-400044−4i4i−4i4i2000000-2-6600000−6i6i2i−2i00000000000000000000000000000000000000000000000000000000000
χ938-8−8i8i0008-4000-84−8i8i4i−4i-400000040000000004i−4i00000000000000000000000000000000000000000000000000000000000
χ948-8−8i8i000-480004-84i−4i−8i8i-400000040000000004i−4i00000000000000000000000000000000000000000000000000000000000
χ958-8−8i8i000-4-4000444i−4i4i−4i2000000-26-600000−6i6i−2i2i00000000000000000000000000000000000000000000000000000000000
χ968-8−8i8i000-4-4000444i−4i4i−4i2000000-2-66000006i−6i−2i2i00000000000000000000000000000000000000000000000000000000000

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