Finite Group Databasebeta

← Group #11713004

Character table — Group #11713004

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size11112222223333444466666666666666888812121212121212121212121212121212161616161616242424242424242432323232
order12224488882222444444444444448888366622444444888888881212242424244444444412121212
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111-1-1-1-1-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ311111111111111-1-1-1-111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ5111111-1-1-1-1111111-1-11111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-1
χ6111111-1-1-1-1111111-1-11-1-1-1-1-1-1-1-11-1-1-1-11111-1-111-1-1-1-11111111111-1-1-1-1-1-111-1-11111-1-1
χ7111111-1-1-1-11111-1-1111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-111
χ8111111-1-1-1-11111-1-1111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-11111111111-1-1-1-111-1-111-1-1-1-111
χ911-1-1-1111-1-111-1-1i−ii−i-111-1-111-1-1111-1-111-1-11-1i−ii−i1-111-1-111-1-1-1111-1-1i−ii−ii−ii−ii−ii−i
χ1011-1-1-1111-1-111-1-1i−ii−i-1-1-111-1-111111-1-111-1-1-11i−ii−i-11-1-111-1-111-1111-1-1−ii−ii−ii−iii−ii−i
χ1111-1-1-1111-1-111-1-1−ii−ii-111-1-111-1-1111-1-111-1-11-1−ii−ii1-111-1-111-1-1-1111-1-1−ii−ii−ii−ii−ii−ii
χ1211-1-1-1111-1-111-1-1−ii−ii-1-1-111-1-111111-1-111-1-1-11−ii−ii-11-1-111-1-111-1111-1-1i−ii−ii−ii−i−ii−ii
χ1311-1-1-11-1-11111-1-1i−i−ii-111-1-111-1-11-1-11111-1-11-1i−i−ii1-1-1-111-1-111-11-1-111i−i−iii−i−iii−i−ii
χ1411-1-1-11-1-11111-1-1i−i−ii-1-1-111-1-1111-1-11111-1-1-11i−i−ii-1111-1-111-1-1-11-1-111−iii−i−iii−ii−i−ii
χ1511-1-1-11-1-11111-1-1−iii−i-111-1-111-1-11-1-11111-1-11-1−iii−i1-1-1-111-1-111-11-1-111−iii−i−iii−i−iii−i
χ1611-1-1-11-1-11111-1-1−iii−i-1-1-111-1-1111-1-11111-1-1-11−iii−i-1111-1-111-1-1-11-1-111i−i−iii−i−ii−iii−i
χ1722222222222222222220000000022222-1-1-1-10022220000000000-1-1-1-1-1-100000000-1-1-1-1
χ1822222222222222-2-2-2-220000000022222-1-1-1-100-2-2-2-20000000000-1-1-1-1-1-1000000001111
χ19222222-2-2-2-2222222-2-22000000002-2-2-2-2-1-1-1-10022-2-20000000000-1-1111100000000-1-111
χ20222222-2-2-2-22222-2-2222000000002-2-2-2-2-1-1-1-100-2-2220000000000-1-111110000000011-1-1
χ212222-2-2000022220000-222222222-200002222-2-20000-2-200000000-2-20000000000000000
χ222222-2-2000022220000-2-2-2-2-2-2-2-2-2-2000022222200002200000000-2-20000000000000000
χ2322-2-22-2000022-2-20000222-2-222-2-2-2000022-2-2-220000-22000000002-20000000000000000
χ2422-2-22-2000022-2-200002-2-222-2-222-2000022-2-22-200002-2000000002-20000000000000000
χ2522-2-2-2222-2-222-2-22i−2i2i−2i-200000000222-2-2-1-111002i−2i2i−2i00000000001-1-1-11100000000−ii−ii
χ2622-2-2-2222-2-222-2-2−2i2i−2i2i-200000000222-2-2-1-11100−2i2i−2i2i00000000001-1-1-11100000000i−ii−i
χ2722-2-2-22-2-22222-2-22i−2i−2i2i-2000000002-2-222-1-111002i−2i−2i2i00000000001-111-1-100000000−iii−i
χ2822-2-2-22-2-22222-2-2−2i2i2i−2i-2000000002-2-222-1-11100−2i2i2i−2i00000000001-111-1-100000000i−i−ii
χ292-22-200i2−i2i2−i22-22-2000002i−2i2i−2i2i−2i2i−2i0i2−i2i2−i22-22-2000000002−22−22−22−200i2−i2i2−i2000000000000
χ302-22-200i2−i2i2−i22-22-200000−2i2i−2i2i−2i2i−2i2i0i2−i2i2−i22-22-200000000−22−22−22−2200i2−i2i2−i2000000000000
χ312-22-200−i2i2−i2i22-22-2000002i−2i2i−2i2i−2i2i−2i0−i2i2−i2i22-22-200000000−22−22−22−2200−i2i2−i2i2000000000000
χ322-22-200−i2i2−i2i22-22-200000−2i2i−2i2i−2i2i−2i2i0−i2i2−i2i22-22-2000000002−22−22−22−200−i2i2−i2i2000000000000
χ332-2-2200i2−i2−i2i22-2-22000002i−2i−2i2i2i−2i−2i2i0i2−i2−i2i22-2-22000000002−2−222−2−2200i2−i2−i2i2000000000000
χ342-2-2200i2−i2−i2i22-2-2200000−2i2i2i−2i−2i2i2i−2i0i2−i2−i2i22-2-2200000000−222−2−222−200i2−i2−i2i2000000000000
χ352-2-2200−i2i2i2−i22-2-22000002i−2i−2i2i2i−2i−2i2i0−i2i2i2−i22-2-2200000000−222−2−222−200−i2i2i2−i2000000000000
χ362-2-2200−i2i2i2−i22-2-2200000−2i2i2i−2i−2i2i2i−2i0−i2i2i2−i22-2-22000000002−2−222−2−2200−i2i2i2−i2000000000000
χ373333333333-1-1-1-13333-11111-1-1-1-1-1-1-1-1-1000011-1-1-1-1-1-11111-1-1-1-10000001111-1-1-1-10000
χ383333333333-1-1-1-13333-1-1-1-1-11111-1-1-1-1-10000-1-1-1-1-1-111-1-1-1-11111000000-1-1-1-111110000
χ393333333333-1-1-1-1-3-3-3-3-11111-1-1-1-1-1-1-1-1-10000111111-1-11111-1-1-1-1000000-1-1-1-111110000
χ403333333333-1-1-1-1-3-3-3-3-1-1-1-1-11111-1-1-1-1-10000-1-1111111-1-1-1-111110000001111-1-1-1-10000
χ41333333-3-3-3-3-1-1-1-133-3-3-11111-1-1-1-1-11111000011-1-111-1-1-1-1-1-1111100000011-1-1-1-1110000
χ42333333-3-3-3-3-1-1-1-133-3-3-1-1-1-1-11111-111110000-1-1-1-111111111-1-1-1-1000000-1-11111-1-10000
χ43333333-3-3-3-3-1-1-1-1-3-333-11111-1-1-1-1-1111100001111-1-1-1-1-1-1-1-11111000000-1-11111-1-10000
χ44333333-3-3-3-3-1-1-1-1-3-333-1-1-1-1-11111-111110000-1-111-1-1111111-1-1-1-100000011-1-1-1-1110000
χ4533-3-3-3333-3-3-1-1113i−3i3i−3i111-1-1-1-111-1-1-11100001-1−ii−ii-1111-1-1-1-111000000i−ii−i−ii−ii0000
χ4633-3-3-3333-3-3-1-1113i−3i3i−3i1-1-11111-1-1-1-1-1110000-11−ii−ii1-1-1-11111-1-1000000−ii−iii−ii−i0000
χ4733-3-3-3333-3-3-1-111−3i3i−3i3i111-1-1-1-111-1-1-11100001-1i−ii−i-1111-1-1-1-111000000−ii−iii−ii−i0000
χ4833-3-3-3333-3-3-1-111−3i3i−3i3i1-1-11111-1-1-1-1-1110000-11i−ii−i1-1-1-11111-1-1000000i−ii−i−ii−ii0000
χ4933-3-3-33-3-333-1-1113i−3i−3i3i111-1-1-1-111-111-1-100001-1−iii−i-11-1-11111-1-1000000i−i−ii−iii−i0000
χ5033-3-3-33-3-333-1-1113i−3i−3i3i1-1-11111-1-1-111-1-10000-11−iii−i1-111-1-1-1-111000000−iii−ii−i−ii0000
χ5133-3-3-33-3-333-1-111−3i3i3i−3i111-1-1-1-111-111-1-100001-1i−i−ii-11-1-11111-1-1000000−iii−ii−i−ii0000
χ5233-3-3-33-3-333-1-111−3i3i3i−3i1-1-11111-1-1-111-1-10000-11i−i−ii1-111-1-1-1-111000000i−i−ii−iii−i0000
χ534444-4-4000044440000-400000000-40000-2-2-2-20000000000000000220000000000000000
χ5444-4-44-4000044-4-40000400000000-40000-2-2220000000000000000-220000000000000000
χ554-44-4002i2−2i22i2−2i24-44-4000000000000002i2−2i22i2−2i2-22-22000000000000000000−i2i2−i2i2000000000000
χ564-44-400−2i22i2−2i22i24-44-400000000000000−2i22i2−2i22i2-22-22000000000000000000i2−i2i2−i2000000000000
χ574-4-44002i2−2i2−2i22i24-4-44000000000000002i2−2i2−2i22i2-222-2000000000000000000−i2i2i2−i2000000000000
χ584-4-4400−2i22i22i2−2i24-4-4400000000000000−2i22i22i2−2i2-222-2000000000000000000i2−i2−i2i2000000000000
χ596666-6-60000-2-2-2-2000022222-2-2-2-2200000000-2-200002200000000000000000000000000
χ606666-6-60000-2-2-2-200002-2-2-2-22222200000000220000-2-200000000000000000000000000
χ6166-6-66-60000-2-2220000-222-2-2-2-222200000000-2200002-200000000000000000000000000
χ6266-6-66-60000-2-2220000-2-2-22222-2-22000000002-20000-2200000000000000000000000000
χ636-66-6003i2−3i23i2−3i2-22-22000002i−2i2i−2i−2i2i−2i2i0−i2i2−i2i20000000000002−22−2−22−22000000000000000000
χ646-66-6003i2−3i23i2−3i2-22-2200000−2i2i−2i2i2i−2i2i−2i0−i2i2−i2i2000000000000−22−222−22−2000000000000000000
χ656-66-600−3i23i2−3i23i2-22-22000002i−2i2i−2i−2i2i−2i2i0i2−i2i2−i2000000000000−22−222−22−2000000000000000000
χ666-66-600−3i23i2−3i23i2-22-2200000−2i2i−2i2i2i−2i2i−2i0i2−i2i2−i20000000000002−22−2−22−22000000000000000000
χ676-6-66003i2−3i2−3i23i2-222-2000002i−2i−2i2i−2i2i2i−2i0−i2i2i2−i20000000000002−2−22−222−2000000000000000000
χ686-6-66003i2−3i2−3i23i2-222-200000−2i2i2i−2i2i−2i−2i2i0−i2i2i2−i2000000000000−222−22−2−22000000000000000000
χ696-6-6600−3i23i23i2−3i2-222-2000002i−2i−2i2i−2i2i2i−2i0i2−i2−i2i2000000000000−222−22−2−22000000000000000000
χ706-6-6600−3i23i23i2−3i2-222-200000−2i2i2i−2i2i−2i−2i2i0i2−i2−i2i20000000000002−2−22−222−2000000000000000000

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