Finite Group Databasebeta

← Group #10714587

Character table — Group #10714587

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size112222222222222444444444444488888888888888161616161616161616161616242424242424242448484848
order122223444468812126668881212122424242416161616242448484848484848482466881212242424244488161616162288
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ922222222222-2-222222-2-2-2222-2-2-2-20000-2-20000000000000000000022-2-200000000
χ1022222222222-2-222222-2-2-2222-2-2-2-20000-2-200000000000000000000-2-22200000000
χ11222222-2-2-2-2200-2-2222000-2-2-20000−i2−i2i2i200−i2−i2−i2−i2i2i2i2i20000000000002-200−i2−i2i2i20000
χ12222222-2-2-2-2200-2-2222000-2-2-20000−i2−i2i2i200−i2−i2−i2−i2i2i2i2i2000000000000-2200i2i2−i2−i20000
χ13222222-2-2-2-2200-2-2222000-2-2-20000i2i2−i2−i200i2i2i2i2−i2−i2−i2−i20000000000002-200i2i2−i2−i20000
χ14222222-2-2-2-2200-2-2222000-2-2-20000i2i2−i2−i200i2i2i2i2−i2−i2−i2−i2000000000000-2200−i2−i2i2i20000
χ1522222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1000000000000
χ1622222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-211-2-2111111000000000000
χ1722222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-1-1-2-2-1-11111000000000000
χ1822222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2112211-1-1-1-1000000000000
χ19222-2-2222-2-2222222-2-22-2-2-22-222220000-2-20000000000000000000000002i−2i2i−2i0000
χ20222-2-2222-2-2222222-2-22-2-2-22-222220000-2-2000000000000000000000000−2i2i−2i2i0000
χ21222-2-2222-2-22-2-2222-2-2-222-22-2-2-2-2-22i−2i2i−2i222i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ22222-2-2222-2-22-2-2222-2-2-222-22-2-2-2-2-2−2i2i−2i2i22−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ23222-2-22-2-222200-2-22-2-20002-2200002−2−220022−2−2−2−222000000000000002-22−2−220000
χ24222-2-22-2-222200-2-22-2-20002-2200002−2−220022−2−2−2−22200000000000000-22−222−20000
χ25222-2-22-2-222200-2-22-2-20002-220000−222−200−2−22222−2−2000000000000002-2−222−20000
χ26222-2-22-2-222200-2-22-2-20002-220000−222−200−2−22222−2−200000000000000-222−2−220000
χ27222-2-2-122-2-2-1-2-2-1-1-111-2221-1111112i−2i2i−2i-1-1−i−iii−i−iii00−i3i300−i3i333−3−3000000000000
χ28222-2-2-122-2-2-1-2-2-1-1-111-2221-1111112i−2i2i−2i-1-1−i−iii−i−iii00i3−i300i3−i3−3−333000000000000
χ29222-2-2-122-2-2-1-2-2-1-1-111-2221-111111−2i2i−2i2i-1-1ii−i−iii−i−i00−i3i300−i3i3−3−333000000000000
χ30222-2-2-122-2-2-1-2-2-1-1-111-2221-111111−2i2i−2i2i-1-1ii−i−iii−i−i00i3−i300i3−i333−3−3000000000000
χ3122-22-22-22-22222-2-2-22-2-2-2222-2-2-22200002-20000000000000000000000000000002-2
χ3222-22-22-22-22222-2-2-22-2-2-2222-2-2-22200002-2000000000000000000000000000000-22
χ3322-22-22-22-222-2-2-2-2-22-222-222-222-2-20000-220000000000002i−2i002i−2i2i−2i000000000000
χ3422-22-22-22-222-2-2-2-2-22-222-222-222-2-20000-22000000000000−2i2i00−2i2i−2i2i000000000000
χ3522-22-2-1-22-22-1-2-2111-1122-2-1-11-1-11100001-13−33−33−33−300−i3i32i−2ii3−i3−ii−ii000000000000
χ3622-22-2-1-22-22-1-2-2111-1122-2-1-11-1-11100001-13−33−33−33−300i3−i3−2i2i−i3i3i−ii−i000000000000
χ3722-22-2-1-22-22-1-2-2111-1122-2-1-11-1-11100001-1−33−33−33−3300−i3i3−2i2ii3−i3i−ii−i000000000000
χ3822-22-2-1-22-22-1-2-2111-1122-2-1-11-1-11100001-1−33−33−33−3300i3−i32i−2i−i3i3−ii−ii000000000000
χ3922-2-222-222-2222-2-2-2-22-22-2-222-2-2220000-22000000002-22200-2-20000000000000000
χ4022-2-222-222-2222-2-2-2-22-22-2-222-2-2220000-2200000000-22-2-200220000000000000000
χ4122-2-222-222-22-2-2-2-2-2-222-22-22222-2-200002-200000000000000000000000000002-200
χ4222-2-222-222-22-2-2-2-2-2-222-22-22222-2-200002-20000000000000000000000000000-2200
χ4322-2-22-1-222-2-1221111-1-22-21-1-111-1-100001-1−i3i3i3−i3−i3i3i3−i32-2-1-10011−i3i3i3−i3000000000000
χ4422-2-22-1-222-2-1221111-1-22-21-1-111-1-100001-1−i3i3i3−i3−i3i3i3−i3-221100-1-1i3−i3−i3i3000000000000
χ4522-2-22-1-222-2-1221111-1-22-21-1-111-1-100001-1i3−i3−i3i3i3−i3−i3i32-2-1-10011i3−i3−i3i3000000000000
χ4622-2-22-1-222-2-1221111-1-22-21-1-111-1-100001-1i3−i3−i3i3i3−i3−i3i3-221100-1-1−i3i3i3−i3000000000000
χ4744444-24444-2-4-4-2-2-2-2-2-4-4-4-2-2-2222200002200000000000000000000000000000000
χ4844444-2-4-4-4-4-20022-2-2-20002220000−2i2−2i22i22i200i2i2i2i2−i2−i2−i2−i2000000000000000000000000
χ4944444-2-4-4-4-4-20022-2-2-200022200002i22i2−2i2−2i200−i2−i2−i2−i2i2i2i2i2000000000000000000000000
χ50444-4-4-244-4-4-244-2-2-2224-4-42-22-2-2-2-200002200000000000000000000000000000000
χ51444-4-4-2-4-444-20022-222000-22-2000022−22−222200−2−22222−2−2000000000000000000000000
χ52444-4-4-2-4-444-20022-222000-22-20000−222222−220022−2−2−2−222000000000000000000000000
χ5344-44-444-44-440044-44-4000-4-44000000000000000000000000000000000000000000
χ5444-44-4-24-44-4-200-2-22-2200022-20000000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ5544-44-4-24-44-4-200-2-22-2200022-20000000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ5644-44-4-2-44-44-244222-22-4-44-2-2222-2-20000-2200000000000000000000000000000000
χ5744-4-4444-4-4440044-4-440004-4-4000000000000000000000000000000000000000000
χ5844-4-44-24-4-44-200-2-222-2000-22200000000006−6−66−666−6000000000000000000000000
χ5944-4-44-24-4-44-200-2-222-2000-2220000000000−666−66−6−66000000000000000000000000
χ6044-4-44-2-444-4-2-4-42222-24-442-2-2-2-2220000-2200000000000000000000000000000000
χ618-800080000-842−42000000000000042−4200000000000000000000000000000000000000
χ628-800080000-8−42420000000000000−424200000000000000000000000000000000000000
χ638-8000-40000442−4243−4300000000026−26−222200000000000000000000000000000000000000
χ648-8000-40000442−42−4343000000000−2626−222200000000000000000000000000000000000000
χ658-8000-400004−424243−43000000000−262622−2200000000000000000000000000000000000000
χ668-8000-400004−4242−434300000000026−2622−2200000000000000000000000000000000000000

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