Finite Group Databasebeta

← Group #13167383

Character table — Group #13167383

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222444444448888888888888888888899991818181818181818181818181818181818181818181818181818181818181818181836363636363636367272727272727272
order12223446661212121233666666336666661212121212121212121212122222444444444466661212121212121212121212121212121212121212444444441212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ611111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ711111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ811111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ91-1-1111-1-1-1111-1-111-1-1-11-1111-1-1-1-1111-11-11111-1-1-1-111-1-11-1ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−i1-11-1i−ii−i1-11-1
χ101-1-1111-1-1-1111-1-111-1-1-11-1111-1-1-1-1111-11-11111-1-1-1-111-1-11-1ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii-11-11−ii−ii-11-11
χ111-1-1111-1-1-1111-1-111-1-1-11-1111-1-1-1-1111-11-11111-1-1-1-111-1-11-1−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−i-11-11i−ii−i-11-11
χ121-1-1111-1-1-1111-1-111-1-1-11-1111-1-1-1-1111-11-11111-1-1-1-111-1-11-1−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii1-11-1−ii−ii1-11-1
χ131-1-111-11-1-11-1-11111-1-1-11-1111-1-1-1-111-11-11-1-1-1-1111111-1-1-11ii−i−i−i−iii11-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiii−i−ii1-1-11i−i−ii1-1-11
χ141-1-111-11-1-11-1-11111-1-1-11-1111-1-1-1-111-11-11-1-1-1-1111111-1-1-11ii−i−i−i−iii11-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−iii−i-111-1−iii−i-111-1
χ151-1-111-11-1-11-1-11111-1-1-11-1111-1-1-1-111-11-11-1-1-1-1111111-1-1-11−i−iiiii−i−i11-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−ii−i−ii-111-1i−i−ii-111-1
χ161-1-111-11-1-11-1-11111-1-1-11-1111-1-1-1-111-11-11-1-1-1-1111111-1-1-11−i−iiiii−i−i11-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−iii−i1-1-11−iii−i1-1-11
χ17222222222222222222222222222222222222222222-2-2-2-2-2-200000000-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1822222-2-2222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22200000000-2-2-2-2222200000000000000000000000000000000
χ192222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ202222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ212222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2000000001111111133−3−333−3−333−3−333−3−30000000000000000
χ222222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-20000000011111111−3−333−3−333−3−333−3−3330000000000000000
χ232222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-2111111112222-2-22222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1111111110000000000000000
χ242222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-2111111112222-2-2-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-10000000000000000
χ252222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-222000000001111-1-1-1-133−3−333−3−3−3−333−3−3330000000000000000
χ262222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-222000000001111-1-1-1-1−3−333−3−33333−3−333−3−30000000000000000
χ2722-2-22002-2-200002222-2-2-2-22222-2-2-2-20000000000002-22-20000002-22-22-22-20000000000002-22-22-22-20000000000000000
χ2822-2-22002-2-200002222-2-2-2-22222-2-2-2-20000000000002-22-2000000-22-222-22-2000000000000-22-22-22-220000000000000000
χ2922-2-22002-2-200002222-2-2-2-22222-2-2-2-2000000000000-22-22002-22-20000-22-2200002-22-22-22-2000000000000000000000000
χ3022-2-22002-2-200002222-2-2-2-22222-2-2-2-2000000000000-22-2200-22-220000-22-220000-22-22-22-22000000000000000000000000
χ3122-2-2-100-1113−33−32222-2-2-2-2-1-1-1-11111000033−3−333−3−32-22-20000002-22-2-11-113−33−33−3−333−3−33-11-11-11-110000000000000000
χ3222-2-2-100-1113−33−32222-2-2-2-2-1-1-1-11111000033−3−333−3−32-22-2000000-22-22-11-113−33−3−333−3−333−31-11-11-11-10000000000000000
χ3322-2-2-100-1113−33−32222-2-2-2-2-1-1-1-11111000033−3−333−3−3-22-22002-22-200001-11-1−33−33-11-11-11-11−333−3−333−30000000000000000
χ3422-2-2-100-1113−33−32222-2-2-2-2-1-1-1-11111000033−3−333−3−3-22-2200-22-2200001-11-1−33−331-11-11-11-13−3−333−3−330000000000000000
χ3522-2-2-100-111−33−332222-2-2-2-2-1-1-1-111110000−3−333−3−3332-22-20000002-22-2-11-11−33−33−333−3−333−3-11-11-11-110000000000000000
χ3622-2-2-100-111−33−332222-2-2-2-2-1-1-1-111110000−3−333−3−3332-22-2000000-22-22-11-11−33−333−3−333−3−331-11-11-11-10000000000000000
χ3722-2-2-100-111−33−332222-2-2-2-2-1-1-1-111110000−3−333−3−333-22-22002-22-200001-11-13−33−3-11-11-11-113−3−333−3−330000000000000000
χ3822-2-2-100-111−33−332222-2-2-2-2-1-1-1-111110000−3−333−3−333-22-2200-22-2200001-11-13−33−31-11-11-11-1−333−3−333−30000000000000000
χ392-22-2200-22-2000022-2-22-22-222-2-222-2-20000000000002-2-220000002i−2i−2i2i2-2-220000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ402-22-2200-22-2000022-2-22-22-222-2-222-2-20000000000002-2-22000000−2i2i2i−2i2-2-22000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ412-22-2200-22-2000022-2-22-22-222-2-222-2-2000000000000-222-2002i−2i−2i2i0000-222-200002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ422-22-2200-22-2000022-2-22-22-222-2-222-2-2000000000000-222-200−2i2i2i−2i0000-222-20000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ432-22-2-1001-113−3−3322-2-22-22-2-1-111-1-111000033−3−3−3−3332-2-220000002i−2i−2i2i-111-13−3−33i3−i3−i3i3−i3i3i3−i3−ii−iii−ii−i0000000000000000
χ442-22-2-1001-113−3−3322-2-22-22-2-1-111-1-111000033−3−3−3−3332-2-22000000−2i2i2i−2i-111-13−3−33−i3i3i3−i3i3−i3−i3i3i−ii−i−ii−ii0000000000000000
χ452-22-2-1001-113−3−3322-2-22-22-2-1-111-1-111000033−3−3−3−333-222-2002i−2i−2i2i00001-1-11−333−3−ii−iii−ii−i−i3i3i3−i3i3−i3−i3i30000000000000000
χ462-22-2-1001-113−3−3322-2-22-22-2-1-111-1-111000033−3−3−3−333-222-200−2i2i2i−2i00001-1-11−333−3i−ii−i−ii−iii3−i3−i3i3−i3i3i3−i30000000000000000
χ472-22-2-1001-11−333−322-2-22-22-2-1-111-1-1110000−3−33333−3−32-2-220000002i−2i−2i2i-111-1−333−3−i3i3i3−i3i3−i3−i3i3−ii−iii−ii−i0000000000000000
χ482-22-2-1001-11−333−322-2-22-22-2-1-111-1-1110000−3−33333−3−32-2-22000000−2i2i2i−2i-111-1−333−3i3−i3−i3i3−i3i3i3−i3i−ii−i−ii−ii0000000000000000
χ492-22-2-1001-11−333−322-2-22-22-2-1-111-1-1110000−3−33333−3−3-222-2002i−2i−2i2i00001-1-113−3−33−ii−iii−ii−ii3−i3−i3i3−i3i3i3−i30000000000000000
χ502-22-2-1001-11−333−322-2-22-22-2-1-111-1-1110000−3−33333−3−3-222-200−2i2i2i−2i00001-1-113−3−33i−ii−i−ii−ii−i3i3i3−i3i3−i3−i3i30000000000000000
χ512-2-2222-2-2-2222-2-222-2-2-22-2222-2-2-2-2222-22-22222-2-2-2-2-2-222-2200000000-2-222-2-22200000000000000000000000000000000
χ522-2-222-22-2-22-2-22222-2-2-22-2222-2-2-2-222-22-22-2-2-2-22222-2-2222-200000000-2-22222-2-200000000000000000000000000000000
χ532-2-22-12-211-1-1-11122-2-2-22-22-1-11111-1-12-22-2-1-1-1-1111122-2-22-22i2i−2i−2i2i2i−2i−2i-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ542-2-22-12-211-1-1-11122-2-2-22-22-1-11111-1-12-22-2-1-1-1-1111122-2-22-2−2i−2i2i2i−2i−2i2i2i-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ552-2-22-12-211-1-1-11122-2-2-22-22-1-11111-1-12-22-2-1-1-1-11111-2-222-220000000011-1-111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ562-2-22-12-211-1-1-11122-2-2-22-22-1-11111-1-12-22-2-1-1-1-11111-2-222-220000000011-1-111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ572-2-22-1-2211-111-1-122-2-2-22-22-1-11111-1-1-22-221111-1-1-1-122-2-2-222i2i−2i−2i−2i−2i2i2i-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ582-2-22-1-2211-111-1-122-2-2-22-22-1-11111-1-1-22-221111-1-1-1-122-2-2-22−2i−2i2i2i2i2i−2i−2i-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ592-2-22-1-2211-111-1-122-2-2-22-22-1-11111-1-1-22-221111-1-1-1-1-2-2222-20000000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ602-2-22-1-2211-111-1-122-2-2-22-22-1-11111-1-1-22-221111-1-1-1-1-2-2222-20000000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ61444444444444441-21-21-2-211-21-21-21-2-2-2111-21-21-21-200000000000000000000000000000000000000000022220000-1-1-1-1
χ62444444444444441-21-21-2-211-21-21-21-2-2-2111-21-21-21-2000000000000000000000000000000000000000000-2-2-2-200001111
χ6344444444444444-21-21-211-2-21-21-21-2111-2-2-21-21-21-210000000000000000000000000000000000000022220000-1-1-1-10000
χ6444444444444444-21-21-211-2-21-21-21-2111-2-2-21-21-21-2100000000000000000000000000000000000000-2-2-2-2000011110000
χ6544444-4-4444-4-4-4-41-21-21-2-211-21-21-21-222-1-1-12-12-12-1200000000000000000000000000000000000000000022-2-20000-1-111
χ6644444-4-4444-4-4-4-41-21-21-2-211-21-21-21-222-1-1-12-12-12-12000000000000000000000000000000000000000000-2-222000011-1-1
χ6744444-4-4444-4-4-4-4-21-21-211-2-21-21-21-21-1-1222-12-12-12-10000000000000000000000000000000000000022-2-20000-1-1110000
χ6844444-4-4444-4-4-4-4-21-21-211-2-21-21-21-21-1-1222-12-12-12-100000000000000000000000000000000000000-2-222000011-1-10000
χ694-4-4444-4-4-4444-4-41-2-12-1-2211-2-12-121-2-221-11-21-2-12-120000000000000000000000000000000000000000002-22-20000-11-11
χ704-4-4444-4-4-4444-4-41-2-12-1-2211-2-12-121-2-221-11-21-2-12-12000000000000000000000000000000000000000000-22-2200001-11-1
χ714-4-4444-4-4-4444-4-4-212-121-1-2-212-12-1-211-1-22-21-212-12-1000000000000000000000000000000000000002i−2i2i−2i0000−ii−ii0000
χ724-4-4444-4-4-4444-4-4-212-121-1-2-212-12-1-211-1-22-21-212-12-100000000000000000000000000000000000000−2i2i−2i2i0000i−ii−i0000
χ734-4-444-44-4-44-4-4441-2-12-1-2211-2-12-121-22-2-11-12-121-21-20000000000000000000000000000000000000000002-2-220000-111-1
χ744-4-444-44-4-44-4-4441-2-12-1-2211-2-12-121-22-2-11-12-121-21-2000000000000000000000000000000000000000000-222-200001-1-11
χ754-4-444-44-4-44-4-444-212-121-1-2-212-12-1-21-112-22-12-1-21-21000000000000000000000000000000000000002i−2i−2i2i0000−iii−i0000
χ764-4-444-44-4-44-4-444-212-121-1-2-212-12-1-21-112-22-12-1-21-2100000000000000000000000000000000000000−2i2i2i−2i0000i−i−ii0000
χ778888-488-4-4-4-4-4-4-42-42-42-4-42-12-12-12-12-4-422-12-12-12-12000000000000000000000000000000000000000000000000000000
χ788888-488-4-4-4-4-4-4-4-42-42-422-42-12-12-12-122-4-42-12-12-12-1000000000000000000000000000000000000000000000000000000
χ798888-4-8-8-4-4-444442-42-42-4-42-12-12-12-1244-2-21-21-21-21-2000000000000000000000000000000000000000000000000000000
χ808888-4-8-8-4-4-44444-42-42-422-42-12-12-12-1-2-244-21-21-21-21000000000000000000000000000000000000000000000000000000
χ8188-8-88008-8-800002-42-4-244-22-42-4-24-24000000000000000000000000000000000000000000000000000000000000000000
χ8288-8-88008-8-80000-42-424-2-24-42-424-24-2000000000000000000000000000000000000000000000000000000000000000000
χ8388-8-8-400-44443−4343−432-42-4-244-2-12-121-21-200003−23−3233−23−323000000000000000000000000000000000000000000000000000000
χ8488-8-8-400-44443−4343−43-42-424-2-242-12-1-21-210000−23323−3−23323−3000000000000000000000000000000000000000000000000000000
χ8588-8-8-400-444−4343−43432-42-4-244-2-12-121-21-20000−3233−23−3233−23000000000000000000000000000000000000000000000000000000
χ8688-8-8-400-444−4343−4343-42-424-2-242-12-1-21-21000023−3−23323−3−233000000000000000000000000000000000000000000000000000000
χ878-88-8800-88-800002-4-2424-4-22-4-242-4-24000000000000000000000000000000000000000000000000000000000000000000
χ888-88-8800-88-80000-424-2-4-224-424-2-424-2000000000000000000000000000000000000000000000000000000000000000000
χ898-88-8-4004-4443−43−43432-4-2424-4-2-121-2-121-200003−23−323−3233−23000000000000000000000000000000000000000000000000000000
χ908-88-8-4004-4443−43−4343-424-2-4-2242-1-212-1-210000−23323−323−3−233000000000000000000000000000000000000000000000000000000
χ918-88-8-4004-44−434343−432-4-2424-4-2-121-2-121-20000−3233−233−23−323000000000000000000000000000000000000000000000000000000
χ928-88-8-4004-44−434343−43-424-2-4-2242-1-212-1-21000023−3−233−23323−3000000000000000000000000000000000000000000000000000000
χ938-8-88-48-844-4-4-4442-4-24-2-442-121-21-2-12-442-2-12-121-21-2000000000000000000000000000000000000000000000000000000
χ948-8-88-48-844-4-4-444-424-242-2-42-1-21-212-12-2-442-12-1-21-21000000000000000000000000000000000000000000000000000000
χ958-8-88-4-8844-444-4-42-4-24-2-442-121-21-2-124-4-221-21-2-12-12000000000000000000000000000000000000000000000000000000
χ968-8-88-4-8844-444-4-4-424-242-2-42-1-21-212-1-224-4-21-212-12-1000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).