Finite Group Databasebeta

← Group #10714591

Character table — Group #10714591

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size112222222222222444444444444488888888888888161616161616161616161616242424242424242448484848
order12222344446881212666888121212242424244488121212122424242424248888242424242424242416161616161616162224
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ922222222222-2-222222-2-2-2222-2-2-2-222-2-22222-2-2-2-2-2-2000000000000000000000000
χ1022222222222-2-222222-2-2-2222-2-2-2-2-2-222-2-2-2-22222-2-2000000000000000000000000
χ11222222-2-2-2-2200-2-2222000-2-2-200002-20022-2-2000000000000000000−i2−i2i2i2−i2−i2i2i20000
χ12222222-2-2-2-2200-2-2222000-2-2-200002-20022-2-2000000000000000000i2i2−i2−i2i2i2−i2−i20000
χ13222222-2-2-2-2200-2-2222000-2-2-20000-2200-2-222000000000000000000−i2−i2i2i2i2i2−i2−i20000
χ14222222-2-2-2-2200-2-2222000-2-2-20000-2200-2-222000000000000000000i2i2−i2−i2−i2−i2i2i20000
χ1522222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ1622222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ1722222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-1-2-2-2-211111111-1-122-2-21111-1-1-1-1000000000000
χ1822222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-1-2-2-2-211111111-1-1-2-222-1-1-1-11111000000000000
χ1922222-12222-1-2-2-1-1-1-1-1-2-2-2-1-1-1111122-2-2-1-1-1-11111110000−i3−i3i3i3−i3−i3i3i3000000000000
χ2022222-12222-1-2-2-1-1-1-1-1-2-2-2-1-1-1111122-2-2-1-1-1-11111110000i3i3−i3−i3i3i3−i3−i3000000000000
χ2122222-12222-1-2-2-1-1-1-1-1-2-2-2-1-1-11111-2-2221111-1-1-1-1110000−i3−i3i3i3i3i3−i3−i3000000000000
χ2222222-12222-1-2-2-1-1-1-1-1-2-2-2-1-1-11111-2-2221111-1-1-1-1110000i3i3−i3−i3−i3−i3i3i3000000000000
χ23222-2-2222-2-2222-2-22-2-22-2-222-222-2-20000000000002-200000000000000002i−2i2i−2i0000
χ24222-2-2222-2-2222-2-22-2-22-2-222-222-2-20000000000002-20000000000000000−2i2i−2i2i0000
χ25222-2-2222-2-22-2-2-2-22-2-2-22222-2-2-222000000000000-220000000000002i−2i2i−2i00000000
χ26222-2-2222-2-22-2-2-2-22-2-2-22222-2-2-222000000000000-22000000000000−2i2i−2i2i00000000
χ27222-2-22-2-222200222-2-2000-2-220000002-2000022-2-2000000000000002−2−222−2−220000
χ28222-2-22-2-222200222-2-2000-2-220000002-2000022-2-200000000000000−222−2−222−20000
χ29222-2-22-2-222200222-2-2000-2-22000000-220000-2-222000000000000002−2−22−222−20000
χ30222-2-22-2-222200222-2-2000-2-22000000-220000-2-22200000000000000−222−22−2−220000
χ3122-22-22-222-2222-2-2-22-2-2-22-22222-2-2000000000000-222-20000002-22-2000000000000
χ3222-22-22-222-2222-2-2-22-2-2-22-22222-2-2000000000000-22-22000000-22-22000000000000
χ3322-22-22-222-22-2-2-2-2-22-222-2-222-2-2220000000000002-2002i−2i2i−2i2i−2i0000000000000000
χ3422-22-22-222-22-2-2-2-2-22-222-2-222-2-2220000000000002-200−2i2i−2i2i−2i2i0000000000000000
χ3522-22-2-1-222-2-122111-11-2-221-1-1-1-11100003−33−33−33−31-12-2003−3−33-11-11000000000000
χ3622-22-2-1-222-2-122111-11-2-221-1-1-1-11100003−33−33−33−31-1-2200−333−31-11-1000000000000
χ3722-22-2-1-222-2-122111-11-2-221-1-1-1-1110000−33−33−33−331-12-200−333−3-11-11000000000000
χ3822-22-2-1-222-2-122111-11-2-221-1-1-1-1110000−33−33−33−331-1-22003−3−331-11-1000000000000
χ3922-22-2-1-222-2-1-2-2111-1122-21-1-111-1-100003−33−3−33−33-11002i−2i−ii−ii−i3i3i3−i3000000000000
χ4022-22-2-1-222-2-1-2-2111-1122-21-1-111-1-100003−33−3−33−33-1100−2i2ii−ii−ii3−i3−i3i3000000000000
χ4122-22-2-1-222-2-1-2-2111-1122-21-1-111-1-10000−33−333−33−3-11002i−2i−ii−iii3−i3−i3i3000000000000
χ4222-22-2-1-222-2-1-2-2111-1122-21-1-111-1-10000−33−333−33−3-1100−2i2ii−ii−i−i3i3i3−i3000000000000
χ4322-2-222-22-2222222-2-22-22-2-22-22222000000000000-2-200000000000000000000002-2
χ4422-2-222-22-2222222-2-22-22-2-22-22222000000000000-2-20000000000000000000000-22
χ4522-2-222-22-222-2-222-2-222-22-22-2-2-2-2-200000000000022000000000000000000002-200
χ4622-2-222-22-222-2-222-2-222-22-22-2-2-2-2-20000000000002200000000000000000000-2200
χ4744444-2-4-4-4-4-20022-2-2-200022200004-400-2-222000000000000000000000000000000
χ4844444-2-4-4-4-4-20022-2-2-20002220000-440022-2-2000000000000000000000000000000
χ49444-4-4-244-4-4-24422-2224-4-4-2-22-2-222000000000000-22000000000000000000000000
χ50444-4-4-244-4-4-2-4-422-222-444-2-2222-2-20000000000002-2000000000000000000000000
χ51444-4-4-2-4-444-200-2-2-22200022-20000004-40000-2-22200000000000000000000000000
χ52444-4-4-2-4-444-200-2-2-22200022-2000000-44000022-2-200000000000000000000000000
χ5344-44-444-4-4440044-44-40004-4-4000000000000000000000000000000000000000000
χ5444-44-4-24-4-44-200-2-22-22000-2220000000023−23−2323000000000000000000000000000000
χ5544-44-4-24-4-44-200-2-22-22000-22200000000−232323−23000000000000000000000000000000
χ5644-4-4444-44-4400-4-4-4-440004-44000000000000000000000000000000000000000000
χ5744-4-44-24-44-4-2002222-2000-22-200000000000023−23−232300000000000000000000000000
χ5844-4-44-24-44-4-2002222-2000-22-2000000000000−232323−2300000000000000000000000000
χ5944-4-44-2-44-44-244-2-222-2-44-42-22-2-2-2-200000000000022000000000000000000000000
χ6044-4-44-2-44-44-2-4-4-2-222-24-442-222222000000000000-2-2000000000000000000000000
χ618-800080000-842−420000000000042−420000000000000000000000000000000000000000
χ628-800080000-8−424200000000000−42420000000000000000000000000000000000000000
χ638-8000-40000442−4243−43000000000−222226−2600000000000000000000000000000000000000
χ648-8000-40000442−42−4343000000000−2222−262600000000000000000000000000000000000000
χ658-8000-400004−424243−4300000000022−22−262600000000000000000000000000000000000000
χ668-8000-400004−4242−434300000000022−2226−2600000000000000000000000000000000000000

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