Finite Group Databasebeta

← Group #13167530

Character table — Group #13167530

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222444444448888888888888888888899991818181818181818181818181818181818181818181818181818181818181818181836363636363636367272727272727272
order1222344666121212123366666633666666121212121212121212121212222244444444446666121212121212121212121212121212121212121222224444666612121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ511111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
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
χ911-1-11i−i1-1-1ii−i−i1111-1-1-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i1-11-1i−i11-1-1ii−i−i1-11-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1-11-1i−ii−i1-11-1i−ii−i
χ1011-1-11i−i1-1-1ii−i−i1111-1-1-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i1-11-1i−i11-1-1ii−i−i1-11-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-11-11−ii−ii-11-11−ii−ii
χ1111-1-11i−i1-1-1ii−i−i1111-1-1-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i1-11-1i−i-1-111−i−iii1-11-1ii−i−i-1-1-1-11111−i−i−i−iiiii1-1-11i−i−ii1-1-11i−i−ii
χ1211-1-11i−i1-1-1ii−i−i1111-1-1-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i1-11-1i−i-1-111−i−iii1-11-1ii−i−i-1-1-1-11111−i−i−i−iiiii-111-1−iii−i-111-1−iii−i
χ1311-1-11−ii1-1-1−i−iii1111-1-1-1-11111-1-1-1-1−i−iii−i−i−i−iiiii1-11-1−ii11-1-1−i−iii1-11-1−i−iii1111-1-1-1-1−i−i−i−iiiii1-11-1−ii−ii1-11-1−ii−ii
χ1411-1-11−ii1-1-1−i−iii1111-1-1-1-11111-1-1-1-1−i−iii−i−i−i−iiiii1-11-1−ii11-1-1−i−iii1-11-1−i−iii1111-1-1-1-1−i−i−i−iiiii-11-11i−ii−i-11-11i−ii−i
χ1511-1-11−ii1-1-1−i−iii1111-1-1-1-11111-1-1-1-1−i−iii−i−i−i−iiiii1-11-1−ii-1-111ii−i−i1-11-1−i−iii-1-1-1-11111iiii−i−i−i−i1-1-11−iii−i1-1-11−iii−i
χ1611-1-11−ii1-1-1−i−iii1111-1-1-1-11111-1-1-1-1−i−iii−i−i−i−iiiii1-11-1−ii-1-111ii−i−i1-11-1−i−iii-1-1-1-11111iiii−i−i−i−i-111-1i−i−ii-111-1i−i−ii
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
χ2722-2-222i−2i2-2-22i2i−2i−2i2222-2-2-2-22222-2-2-2-22i2i−2i−2i2i2i2i2i−2i−2i−2i−2i-22-22−2i2i00000000-22-22−2i−2i2i2i00000000000000000000000000000000
χ2822-2-22−2i2i2-2-2−2i−2i2i2i2222-2-2-2-22222-2-2-2-2−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i-22-222i−2i00000000-22-222i2i−2i−2i00000000000000000000000000000000
χ2922-2-2-12i−2i-111−i−iii2222-2-2-2-2-1-1-1-111112i2i−2i−2i−i−i−i−iiiii2-22-22i−2i22-2-22i2i−2i−2i-11-11−i−iii-1-1-1-11111−i−i−i−iiiii0000000000000000
χ3022-2-2-12i−2i-111−i−iii2222-2-2-2-2-1-1-1-111112i2i−2i−2i−i−i−i−iiiii2-22-22i−2i-2-222−2i−2i2i2i-11-11−i−iii1111-1-1-1-1iiii−i−i−i−i0000000000000000
χ3122-2-2-12i−2i-111−i−iii2222-2-2-2-2-1-1-1-111112i2i−2i−2i−i−i−i−iiiii-22-22−2i2i000000001-11-1ii−i−i33−3−3−3−333i3i3−i3−i3−i3−i3i3i30000000000000000
χ3222-2-2-12i−2i-111−i−iii2222-2-2-2-2-1-1-1-111112i2i−2i−2i−i−i−i−iiiii-22-22−2i2i000000001-11-1ii−i−i−3−33333−3−3−i3−i3i3i3i3i3−i3−i30000000000000000
χ3322-2-2-1−2i2i-111ii−i−i2222-2-2-2-2-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i2-22-2−2i2i22-2-2−2i−2i2i2i-11-11ii−i−i-1-1-1-11111iiii−i−i−i−i0000000000000000
χ3422-2-2-1−2i2i-111ii−i−i2222-2-2-2-2-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i2-22-2−2i2i-2-2222i2i−2i−2i-11-11ii−i−i1111-1-1-1-1−i−i−i−iiiii0000000000000000
χ3522-2-2-1−2i2i-111ii−i−i2222-2-2-2-2-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i-22-222i−2i000000001-11-1−i−iii33−3−3−3−333−i3−i3i3i3i3i3−i3−i30000000000000000
χ3622-2-2-1−2i2i-111ii−i−i2222-2-2-2-2-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i-22-222i−2i000000001-11-1−i−iii−3−33333−3−3i3i3−i3−i3−i3−i3i3i30000000000000000
χ372-22-2200-2-22000022-2-222-2-222-2-2-2-22200000000000022-2-20000002i−2i2i−2i22-2-20000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ382-22-2200-2-22000022-2-222-2-222-2-2-2-22200000000000022-2-2000000−2i2i−2i2i22-2-2000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ392-22-2200-2-22000022-2-222-2-222-2-2-2-222000000000000-2-222002-22-20000-2-22200002-22-22-22-2000000000000000000000000
χ402-22-2200-2-22000022-2-222-2-222-2-2-2-222000000000000-2-22200-22-220000-2-2220000-22-22-22-22000000000000000000000000
χ412-22-2-10011-1−i3i3−i3i322-2-222-2-2-1-11111-1-10000−i3−i3i3i3−i3−i3i3i322-2-20000002i−2i2i−2i-1-111−i3i3−i3i33−3−333−3−33−ii−ii−ii−ii0000000000000000
χ422-22-2-10011-1−i3i3−i3i322-2-222-2-2-1-11111-1-10000−i3−i3i3i3−i3−i3i3i322-2-2000000−2i2i−2i2i-1-111−i3i3−i3i3−333−3−333−3i−ii−ii−ii−i0000000000000000
χ432-22-2-10011-1−i3i3−i3i322-2-222-2-2-1-11111-1-10000−i3−i3i3i3−i3−i3i3i3-2-222002-22-2000011-1-1i3−i3i3−i3-11-11-11-11−i3i3i3−i3−i3i3i3−i30000000000000000
χ442-22-2-10011-1−i3i3−i3i322-2-222-2-2-1-11111-1-10000−i3−i3i3i3−i3−i3i3i3-2-22200-22-22000011-1-1i3−i3i3−i31-11-11-11-1i3−i3−i3i3i3−i3−i3i30000000000000000
χ452-22-2-10011-1i3−i3i3−i322-2-222-2-2-1-11111-1-10000i3i3−i3−i3i3i3−i3−i322-2-20000002i−2i2i−2i-1-111i3−i3i3−i3−333−3−333−3−ii−ii−ii−ii0000000000000000
χ462-22-2-10011-1i3−i3i3−i322-2-222-2-2-1-11111-1-10000i3i3−i3−i3i3i3−i3−i322-2-2000000−2i2i−2i2i-1-111i3−i3i3−i33−3−333−3−33i−ii−ii−ii−i0000000000000000
χ472-22-2-10011-1i3−i3i3−i322-2-222-2-2-1-11111-1-10000i3i3−i3−i3i3i3−i3−i3-2-222002-22-2000011-1-1−i3i3−i3i3-11-11-11-11i3−i3−i3i3i3−i3−i3i30000000000000000
χ482-22-2-10011-1i3−i3i3−i322-2-222-2-2-1-11111-1-10000i3i3−i3−i3i3i3−i3−i3-2-22200-22-22000011-1-1−i3i3−i3i31-11-11-11-1−i3i3i3−i3−i3i3i3−i30000000000000000
χ492-2-22200-22-2000022-2-2-2-22222-2-222-2-20000000000002-2-220000002-2-222-2-220000000000002-22-2-22-220000000000000000
χ502-2-22200-22-2000022-2-2-2-22222-2-222-2-20000000000002-2-22000000-222-22-2-22000000000000-22-222-22-20000000000000000
χ512-2-22200-22-2000022-2-2-2-22222-2-222-2-2000000000000-222-2002-2-220000-222-200002-22-2-22-22000000000000000000000000
χ522-2-22200-22-2000022-2-2-2-22222-2-222-2-2000000000000-222-200-222-20000-222-20000-22-222-22-2000000000000000000000000
χ532-2-22-1001-113−3−3322-2-2-2-222-1-111-1-111000033−3−3−3−3332-2-220000002-2-22-111-13−3−33−333−33−3−33-11-111-11-10000000000000000
χ542-2-22-1001-113−3−3322-2-2-2-222-1-111-1-111000033−3−3−3−3332-2-22000000-222-2-111-13−3−333−3−33−333−31-11-1-11-110000000000000000
χ552-2-22-1001-113−3−3322-2-2-2-222-1-111-1-111000033−3−3−3−333-222-2002-2-2200001-1-11−333−3-11-111-11-13−3−33−333−30000000000000000
χ562-2-22-1001-113−3−3322-2-2-2-222-1-111-1-111000033−3−3−3−333-222-200-222-200001-1-11−333−31-11-1-11-11−333−33−3−330000000000000000
χ572-2-22-1001-11−333−322-2-2-2-222-1-111-1-1110000−3−33333−3−32-2-220000002-2-22-111-1−333−33−3−33−333−3-11-111-11-10000000000000000
χ582-2-22-1001-11−333−322-2-2-2-222-1-111-1-1110000−3−33333−3−32-2-22000000-222-2-111-1−333−3−333−33−3−331-11-1-11-110000000000000000
χ592-2-22-1001-11−333−322-2-2-2-222-1-111-1-1110000−3−33333−3−3-222-2002-2-2200001-1-113−3−33-11-111-11-1−333−33−3−330000000000000000
χ602-2-22-1001-11−333−322-2-2-2-222-1-111-1-1110000−3−33333−3−3-222-200-222-200001-1-113−3−331-11-1-11-113−3−33−333−30000000000000000
χ61444444444444441-21-21-21-21-21-21-21-21-21-21-21-21-21-2000000000000000000000000000000000000000022002200-1-100-1-1
χ62444444444444441-21-21-21-21-21-21-21-21-21-21-21-21-21-20000000000000000000000000000000000000000-2-200-2-200110011
χ6344444444444444-21-21-21-21-21-21-21-21-21-21-21-21-21-210000000000000000000000000000000000000022002200-1-100-1-100
χ6444444444444444-21-21-21-21-21-21-21-21-21-21-21-21-21-2100000000000000000000000000000000000000-2-200-2-20011001100
χ6544444-4-4444-4-4-4-41-21-21-21-21-21-21-21-2-12-12-12-12-12-1200000000000000000000000000000000000000002200-2-200-1-10011
χ6644444-4-4444-4-4-4-41-21-21-21-21-21-21-21-2-12-12-12-12-12-120000000000000000000000000000000000000000-2-20022001100-1-1
χ6744444-4-4444-4-4-4-4-21-21-21-21-21-21-21-212-12-12-12-12-12-1000000000000000000000000000000000000002200-2-200-1-1001100
χ6844444-4-4444-4-4-4-4-21-21-21-21-21-21-21-212-12-12-12-12-12-100000000000000000000000000000000000000-2-20022001100-1-100
χ6944-4-444i−4i4-4-44i4i−4i−4i1-21-2-12-121-21-2-12-12i−2i−i2ii−2ii−2i−i2i−i2i00000000000000000000000000000000000000002-2002i−2i00-1100−ii
χ7044-4-444i−4i4-4-44i4i−4i−4i1-21-2-12-121-21-2-12-12i−2i−i2ii−2ii−2i−i2i−i2i0000000000000000000000000000000000000000-2200−2i2i001-100i−i
χ7144-4-444i−4i4-4-44i4i−4i−4i-21-212-12-1-21-212-12-1−2ii2i−i−2ii−2ii2i−i2i−i000000000000000000000000000000000000002-2002i−2i00-1100−ii00
χ7244-4-444i−4i4-4-44i4i−4i−4i-21-212-12-1-21-212-12-1−2ii2i−i−2ii−2ii2i−i2i−i00000000000000000000000000000000000000-2200−2i2i001-100i−i00
χ7344-4-44−4i4i4-4-4−4i−4i4i4i1-21-2-12-121-21-2-12-12−i2ii−2i−i2i−i2ii−2ii−2i00000000000000000000000000000000000000002-200−2i2i00-1100i−i
χ7444-4-44−4i4i4-4-4−4i−4i4i4i1-21-2-12-121-21-2-12-12−i2ii−2i−i2i−i2ii−2ii−2i0000000000000000000000000000000000000000-22002i−2i001-100−ii
χ7544-4-44−4i4i4-4-4−4i−4i4i4i-21-212-12-1-21-212-12-12i−i−2ii2i−i2i−i−2ii−2ii000000000000000000000000000000000000002-200−2i2i00-1100i−i00
χ7644-4-44−4i4i4-4-4−4i−4i4i4i-21-212-12-1-21-212-12-12i−i−2ii2i−i2i−i−2ii−2ii00000000000000000000000000000000000000-22002i−2i001-100−ii00
χ778888-488-4-4-4-4-4-4-42-42-42-42-4-12-12-12-122-42-4-12-12-12-12000000000000000000000000000000000000000000000000000000
χ788888-488-4-4-4-4-4-4-4-42-42-42-422-12-12-12-1-42-422-12-12-12-1000000000000000000000000000000000000000000000000000000
χ798888-4-8-8-4-4-444442-42-42-42-4-12-12-12-12-24-241-21-21-21-2000000000000000000000000000000000000000000000000000000
χ808888-4-8-8-4-4-44444-42-42-42-422-12-12-12-14-24-2-21-21-21-21000000000000000000000000000000000000000000000000000000
χ8188-8-8-48i−8i-444−4i−4i4i4i2-42-4-24-24-12-121-21-22i−4i−2i4i−i2i−i2ii−2ii−2i000000000000000000000000000000000000000000000000000000
χ8288-8-8-48i−8i-444−4i−4i4i4i-42-424-24-22-12-1-21-21−4i2i4i−2i2i−i2i−i−2ii−2ii000000000000000000000000000000000000000000000000000000
χ8388-8-8-4−8i8i-4444i4i−4i−4i2-42-4-24-24-12-121-21-2−2i4i2i−4ii−2ii−2i−i2i−i2i000000000000000000000000000000000000000000000000000000
χ8488-8-8-4−8i8i-4444i4i−4i−4i-42-424-24-22-12-1-21-214i−2i−4i2i−2ii−2ii2i−i2i−i000000000000000000000000000000000000000000000000000000
χ858-88-8800-8-8800002-4-242-4-242-4-24-242-4000000000000000000000000000000000000000000000000000000000000000000
χ868-88-8800-8-880000-424-2-424-2-424-24-2-42000000000000000000000000000000000000000000000000000000000000000000
χ878-88-8-40044-4−4i34i3−4i34i32-4-242-4-24-121-21-2-120000−i32i3i3−2i3−i32i3i3−2i3000000000000000000000000000000000000000000000000000000
χ888-88-8-40044-4−4i34i3−4i34i3-424-2-424-22-1-21-212-100002i3−i3−2i3i32i3−i3−2i3i3000000000000000000000000000000000000000000000000000000
χ898-88-8-40044-44i3−4i34i3−4i32-4-242-4-24-121-21-2-120000i3−2i3−i32i3i3−2i3−i32i3000000000000000000000000000000000000000000000000000000
χ908-88-8-40044-44i3−4i34i3−4i3-424-2-424-22-1-21-212-10000−2i3i32i3−i3−2i3i32i3−i3000000000000000000000000000000000000000000000000000000
χ918-8-88800-88-800002-4-24-242-42-4-242-4-24000000000000000000000000000000000000000000000000000000000000000000
χ928-8-88800-88-80000-424-24-2-42-424-2-424-2000000000000000000000000000000000000000000000000000000000000000000
χ938-8-88-4004-4443−43−43432-4-24-242-4-121-2-121-200003−23−323−3233−23000000000000000000000000000000000000000000000000000000
χ948-8-88-4004-4443−43−4343-424-24-2-422-1-212-1-210000−23323−323−3−233000000000000000000000000000000000000000000000000000000
χ958-8-88-4004-44−434343−432-4-24-242-4-121-2-121-20000−3233−233−23−323000000000000000000000000000000000000000000000000000000
χ968-8-88-4004-44−434343−43-424-24-2-422-1-212-1-21000023−3−233−23323−3000000000000000000000000000000000000000000000000000000

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