Finite Group Databasebeta

← Group #10802000

Character table — Group #10802000

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222224444444444444444666666666666666688888888888888888888121212121212121216161616161616162424242424242424
order122244442234466612121212444466888888881212888888888888888822448888121212122424242424242424224444446612122424242444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111-11-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-11-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-1-1-1-1-1111111111-11-111-1-1-1-111-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1111111-1-1-1-1-1-1-1-111111111-11-11-1-11111-1-111-1-1
χ911111111111111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1-1-111-1-11111-1-1
χ1011111111111111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1111-1-111-1-1-1-111
χ1111111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1111111111-11-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111-11-1-1-11111-1-1-1-111
χ1211111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-11-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1111-1-1-1-11111-1-1
χ1311111111111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ1411111111111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1511111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1611111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ171111-1-1-1-1-1-1111111-1-1-1-1ii−i−i-1-1ii−i−i11-1-111iiii−i−i−i−i1111-1-1-1-111-1-1i−ii−iii−i−iii−i−i11-1-11-11-1ii−i−i11-1-1i−ii−i1-11-1i−ii−i
χ181111-1-1-1-1-1-1111111-1-1-1-1ii−i−i-1-1ii−i−i11-1-111iiii−i−i−i−i1111-1-1-1-1-1-111−ii−iiii−i−iii−i−i11-1-11-11-1ii−i−i-1-111−ii−ii-11-11−ii−ii
χ191111-1-1-1-1-1-1111111-1-1-1-1ii−i−i-1-1ii−i−i11-1-111−i−i−i−iiiii-1-1-1-1111111-1-1i−ii−iii−i−iii−i−i11-1-1-11-11−i−iii11-1-1i−ii−i-11-11−ii−ii
χ201111-1-1-1-1-1-1111111-1-1-1-1ii−i−i-1-1ii−i−i11-1-111−i−i−i−iiiii-1-1-1-11111-1-111−ii−iiii−i−iii−i−i11-1-1-11-11−i−iii-1-111−ii−ii1-11-1i−ii−i
χ211111-1-1-1-1-1-1111111-1-1-1-1ii−i−i-1-1−i−iii-1-11111iiii−i−i−i−i1111-1-1-1-11-1-11i−i−iiii−i−i−i−iii-1-111-11-11−i−iii1-1-11i−i−ii1-1-11i−i−ii
χ221111-1-1-1-1-1-1111111-1-1-1-1ii−i−i-1-1−i−iii-1-11111iiii−i−i−i−i1111-1-1-1-1-111-1−iii−iii−i−i−i−iii-1-111-11-11−i−iii-111-1−iii−i-111-1−iii−i
χ231111-1-1-1-1-1-1111111-1-1-1-1ii−i−i-1-1−i−iii-1-11111−i−i−i−iiiii-1-1-1-111111-1-11i−i−iiii−i−i−i−iii-1-1111-11-1ii−i−i1-1-11i−i−ii-111-1−iii−i
χ241111-1-1-1-1-1-1111111-1-1-1-1ii−i−i-1-1−i−iii-1-11111−i−i−i−iiiii-1-1-1-11111-111-1−iii−iii−i−i−i−iii-1-1111-11-1ii−i−i-111-1−iii−i1-1-11i−i−ii
χ251111-1-1-1-1-1-1111111-1-1-1-1−i−iii-1-1ii−i−i-1-11111iiii−i−i−i−i-1-1-1-111111-1-11−iii−i−i−iiiii−i−i-1-1111-11-1−i−iii1-1-11−iii−i-111-1i−i−ii
χ261111-1-1-1-1-1-1111111-1-1-1-1−i−iii-1-1ii−i−i-1-11111iiii−i−i−i−i-1-1-1-11111-111-1i−i−ii−i−iiiii−i−i-1-1111-11-1−i−iii-111-1i−i−ii1-1-11−iii−i
χ271111-1-1-1-1-1-1111111-1-1-1-1−i−iii-1-1ii−i−i-1-11111−i−i−i−iiiii1111-1-1-1-11-1-11−iii−i−i−iiiii−i−i-1-111-11-11ii−i−i1-1-11−iii−i1-1-11−iii−i
χ281111-1-1-1-1-1-1111111-1-1-1-1−i−iii-1-1ii−i−i-1-11111−i−i−i−iiiii1111-1-1-1-1-111-1i−i−ii−i−iiiii−i−i-1-111-11-11ii−i−i-111-1i−i−ii-111-1i−i−ii
χ291111-1-1-1-1-1-1111111-1-1-1-1−i−iii-1-1−i−iii11-1-111iiii−i−i−i−i-1-1-1-1111111-1-1−ii−ii−i−iii−i−iii11-1-1-11-11ii−i−i11-1-1−ii−ii-11-11i−ii−i
χ301111-1-1-1-1-1-1111111-1-1-1-1−i−iii-1-1−i−iii11-1-111iiii−i−i−i−i-1-1-1-11111-1-111i−ii−i−i−iii−i−iii11-1-1-11-11ii−i−i-1-111i−ii−i1-11-1−ii−ii
χ311111-1-1-1-1-1-1111111-1-1-1-1−i−iii-1-1−i−iii11-1-111−i−i−i−iiiii1111-1-1-1-111-1-1−ii−ii−i−iii−i−iii11-1-11-11-1−i−iii11-1-1−ii−ii1-11-1−ii−ii
χ321111-1-1-1-1-1-1111111-1-1-1-1−i−iii-1-1−i−iii11-1-111−i−i−i−iiiii1111-1-1-1-1-1-111i−ii−i−i−iii−i−iii11-1-11-11-1−i−iii-1-111i−ii−i-11-11i−ii−i
χ332222222222-122-1-1-1-1-1-1-12222-1-122222222-1-1000000000000000022222222-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-100000000
χ342222222222-122-1-1-1-1-1-1-12222-1-122222222-1-10000000000000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1000000001111111100000000
χ352222222222-122-1-1-1-1-1-1-12222-1-1-2-2-2-2-2-2-2-2-1-100000000000000002-22-222-2-2-1-1-1-11111111100000000-11-11-1-11100000000
χ362222222222-122-1-1-1-1-1-1-12222-1-1-2-2-2-2-2-2-2-2-1-10000000000000000-22-22-2-222-1-1-1-111111111000000001-11-111-1-100000000
χ372222222222-122-1-1-1-1-1-1-1-2-2-2-2-1-12222-2-2-2-2-1-100000000000000002-22-2-2-2221111-1-1-1-1111100000000-11-1111-1-100000000
χ382222222222-122-1-1-1-1-1-1-1-2-2-2-2-1-12222-2-2-2-2-1-10000000000000000-22-2222-2-21111-1-1-1-11111000000001-11-1-1-11100000000
χ392222222222-122-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2-2-22222-1-100000000000000002222-2-2-2-211111111-1-1-1-100000000-1-1-1-1111100000000
χ402222222222-122-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2-2-22222-1-10000000000000000-2-2-2-2222211111111-1-1-1-1000000001111-1-1-1-100000000
χ4122222222-2-22-2-222222220000-2-22-22-20000-2-222-2-222-2-2000000000000000000002-22-200002-2-2200000000000000000000
χ4222222222-2-22-2-222222220000-2-22-22-20000-2-2-2-222-2-222000000000000000000002-22-20000-222-200000000000000000000
χ4322222222-2-22-2-222222220000-2-2-22-220000-2-222-2-222-2-200000000000000000000-22-220000-222-200000000000000000000
χ4422222222-2-22-2-222222220000-2-2-22-220000-2-2-2-222-2-22200000000000000000000-22-2200002-2-2200000000000000000000
χ452222-2-2-2-2222-2-2222-2-2-2-20000222i−2i−2i2i0000-2-22i2i−2i−2i−2i−2i2i2i000000000000000000002i−2i−2i2i000022-2-200000000000000000000
χ462222-2-2-2-2222-2-2222-2-2-2-20000222i−2i−2i2i0000-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000002i−2i−2i2i0000-2-22200000000000000000000
χ472222-2-2-2-2222-2-2222-2-2-2-2000022−2i2i2i−2i0000-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000−2i2i2i−2i0000-2-22200000000000000000000
χ482222-2-2-2-2222-2-2222-2-2-2-2000022−2i2i2i−2i0000-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000−2i2i2i−2i000022-2-200000000000000000000
χ492222-2-2-2-2-2-2-122-1-1-111112i2i−2i−2i112i2i−2i−2i22-2-2-1-1000000000000000022-2-22i−2i2i−2i−i−iii−i−iii-1-11100000000-1-111−ii−ii00000000
χ502222-2-2-2-2-2-2-122-1-1-111112i2i−2i−2i112i2i−2i−2i22-2-2-1-10000000000000000-2-222−2i2i−2i2i−i−iii−i−iii-1-1110000000011-1-1i−ii−i00000000
χ512222-2-2-2-2-2-2-122-1-1-111112i2i−2i−2i11−2i−2i2i2i-2-222-1-100000000000000002-2-222i−2i−2i2i−i−iiiii−i−i11-1-100000000-111-1−iii−i00000000
χ522222-2-2-2-2-2-2-122-1-1-111112i2i−2i−2i11−2i−2i2i2i-2-222-1-10000000000000000-222-2−2i2i2i−2i−i−iiiii−i−i11-1-1000000001-1-11i−i−ii00000000
χ532222-2-2-2-2-2-2-122-1-1-11111−2i−2i2i2i112i2i−2i−2i-2-222-1-100000000000000002-2-22−2i2i2i−2iii−i−i−i−iii11-1-100000000-111-1i−i−ii00000000
χ542222-2-2-2-2-2-2-122-1-1-11111−2i−2i2i2i112i2i−2i−2i-2-222-1-10000000000000000-222-22i−2i−2i2iii−i−i−i−iii11-1-1000000001-1-11−iii−i00000000
χ552222-2-2-2-2-2-2-122-1-1-11111−2i−2i2i2i11−2i−2i2i2i22-2-2-1-1000000000000000022-2-2−2i2i−2i2iii−i−iii−i−i-1-11100000000-1-111i−ii−i00000000
χ562222-2-2-2-2-2-2-122-1-1-11111−2i−2i2i2i11−2i−2i2i2i22-2-2-1-10000000000000000-2-2222i−2i2i−2iii−i−iii−i−i-1-1110000000011-1-1−ii−ii00000000
χ5722-2-222-2-22-22-22-2-22-2-22200002-200002-22-2-222i−2i2i−2i2i−2i2i−2i0000000000000000000000002-22-200002i−2i2i−2i0000000000000000
χ5822-2-222-2-22-22-22-2-22-2-22200002-200002-22-2-22−2i2i−2i2i−2i2i−2i2i0000000000000000000000002-22-20000−2i2i−2i2i0000000000000000
χ5922-2-222-2-22-22-22-2-22-2-22200002-20000-22-22-222i−2i2i−2i2i−2i2i−2i000000000000000000000000-22-220000−2i2i−2i2i0000000000000000
χ6022-2-222-2-22-22-22-2-22-2-22200002-20000-22-22-22−2i2i−2i2i−2i2i−2i2i000000000000000000000000-22-2200002i−2i2i−2i0000000000000000
χ6122-2-222-2-2-2222-2-2-22-2-2222-22-2-22000000002-22i−2i−2i2i2i−2i−2i2i2i2i−2i−2i2i2i−2i−2i000000002-22-200000000000000000000000000000000
χ6222-2-222-2-2-2222-2-2-22-2-2222-22-2-22000000002-2−2i2i2i−2i−2i2i2i−2i−2i−2i2i2i−2i−2i2i2i000000002-22-200000000000000000000000000000000
χ6322-2-222-2-2-2222-2-2-22-2-222-22-22-22000000002-22i−2i−2i2i2i−2i−2i2i−2i−2i2i2i−2i−2i2i2i00000000-22-2200000000000000000000000000000000
χ6422-2-222-2-2-2222-2-2-22-2-222-22-22-22000000002-2−2i2i2i−2i−2i2i2i−2i2i2i−2i−2i2i2i−2i−2i00000000-22-2200000000000000000000000000000000
χ6522-2-2-2-2222-222-2-2-2222-2-22i−2i−2i2i2-2000000002-22-2-22-222-2−2i−2i2i2i2i2i−2i−2i000000002i−2i−2i2i00000000000000000000000000000000
χ6622-2-2-2-2222-222-2-2-2222-2-22i−2i−2i2i2-2000000002-2-222-22-2-222i2i−2i−2i−2i−2i2i2i000000002i−2i−2i2i00000000000000000000000000000000
χ6722-2-2-2-2222-222-2-2-2222-2-2−2i2i2i−2i2-2000000002-22-2-22-222-22i2i−2i−2i−2i−2i2i2i00000000−2i2i2i−2i00000000000000000000000000000000
χ6822-2-2-2-2222-222-2-2-2222-2-2−2i2i2i−2i2-2000000002-2-222-22-2-22−2i−2i2i2i2i2i−2i−2i00000000−2i2i2i−2i00000000000000000000000000000000
χ6922-2-2-2-222-222-22-2-2222-2-20000-2200002-2-22-222-22-2-22-220000000000000000000000002-2-2200002-2-220000000000000000
χ7022-2-2-2-222-222-22-2-2222-2-20000-2200002-2-22-22-22-222-22-20000000000000000000000002-2-220000-222-20000000000000000
χ7122-2-2-2-222-222-22-2-2222-2-20000-220000-222-2-222-22-2-22-22000000000000000000000000-222-20000-222-20000000000000000
χ7222-2-2-2-222-222-22-2-2222-2-20000-220000-222-2-22-22-222-22-2000000000000000000000000-222-200002-2-220000000000000000
χ7344444444-4-4-2-4-4-2-2-2-2-2-2-20000224-44-40000220000000000000000000000000000-22-220000000000000000000000000000
χ7444444444-4-4-2-4-4-2-2-2-2-2-2-2000022-44-4400002200000000000000000000000000002-22-20000000000000000000000000000
χ754444-4-4-4-444-2-4-4-2-2-222220000-2-24i−4i−4i4i0000220000000000000000000000000000−2i2i2i−2i0000000000000000000000000000
χ764444-4-4-4-444-2-4-4-2-2-222220000-2-2−4i4i4i−4i00002200000000000000000000000000002i−2i−2i2i0000000000000000000000000000
χ7744-4-444-4-44-4-2-4422-222-2-20000-2200004-44-42-200000000000000000000000000000000-22-22000000000000000000000000
χ7844-4-444-4-44-4-2-4422-222-2-20000-220000-44-442-2000000000000000000000000000000002-22-2000000000000000000000000
χ7944-4-444-4-4-44-24-422-222-2-24-44-42-200000000-22000000000000000000000000-22-2200000000000000000000000000000000
χ8044-4-444-4-4-44-24-422-222-2-2-44-442-200000000-220000000000000000000000002-22-200000000000000000000000000000000
χ8144-4-4-4-4444-4-24-422-2-2-2224i−4i−4i4i-2200000000-22000000000000000000000000−2i2i2i−2i00000000000000000000000000000000
χ8244-4-4-4-4444-4-24-422-2-2-222−4i4i4i−4i-2200000000-220000000000000000000000002i−2i−2i2i00000000000000000000000000000000
χ8344-4-4-4-444-44-2-4422-2-2-22200002-200004-4-442-200000000000000000000000000000000-222-2000000000000000000000000
χ8444-4-4-4-444-44-2-4422-2-2-22200002-20000-444-42-2000000000000000000000000000000002-2-22000000000000000000000000
χ854-44-44i−4i4i−4i004004-4-44i−4i4i−4i0000000000000000000000002i2−2i22i2−2i222−2222−2200000000000000000000000000000000000000000000
χ864-44-44i−4i4i−4i004004-4-44i−4i4i−4i000000000000000000000000−2i22i2−2i22i2−2222−222200000000000000000000000000000000000000000000
χ874-44-4−4i4i−4i4i004004-4-4−4i4i−4i4i0000000000000000000000002i2−2i22i2−2i2−2222−222200000000000000000000000000000000000000000000
χ884-44-4−4i4i−4i4i004004-4-4−4i4i−4i4i000000000000000000000000−2i22i2−2i22i222−2222−2200000000000000000000000000000000000000000000
χ894-4-444i−4i−4i4i00400-44-4−4i4i4i−4i00000000000000000000000022−22−2222−2i22i22i2−2i200000000000000000000000000000000000000000000
χ904-4-444i−4i−4i4i00400-44-4−4i4i4i−4i000000000000000000000000−222222−222i2−2i2−2i22i200000000000000000000000000000000000000000000
χ914-4-44−4i4i4i−4i00400-44-44i−4i−4i4i00000000000000000000000022−22−22222i2−2i2−2i22i200000000000000000000000000000000000000000000
χ924-4-44−4i4i4i−4i00400-44-44i−4i−4i4i000000000000000000000000−222222−22−2i22i22i2−2i200000000000000000000000000000000000000000000
χ938-88-88i−8i8i−8i00-400-444−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ948-88-8−8i8i−8i8i00-400-4444i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ958-8-888i−8i−8i8i00-4004-444i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ968-8-88−8i8i8i−8i00-4004-44−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000000000

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