Finite Group Databasebeta

← Group #10713921

Character table — Group #10713921

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size112222222222222444444444444488888888888888161616161616161616161616242424242424242448484848
order122223444466688668881212121224242424161616162424484848484848484822666688242424242488161616162444
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
χ51111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111
χ61111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111
χ92222222222222-2-222-2-2-22222-2-2-2-20000-2-20000000000000000000022-2-200000000
χ102222222222222-2-222-2-2-22222-2-2-2-20000-2-200000000000000000000-2-22200000000
χ1122222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1000000000000
χ1222222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-21111-2-21111000000000000
χ1322222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-1-1-1-1-2-21111000000000000
χ1422222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2111122-1-1-1-1000000000000
χ15222-2-2222-2-2-2-22002-200022-2-20000−i2−i2i2i200−i2−i2−i2−i2i2i2i2i2000000000000002i−2i22−2−20000
χ16222-2-2222-2-2-2-22002-200022-2-20000−i2−i2i2i200−i2−i2−i2−i2i2i2i2i200000000000000−2i2i−2−2220000
χ17222-2-2222-2-2-2-22002-200022-2-20000i2i2−i2−i200i2i2i2i2−i2−i2−i2−i2000000000000002i−2i−2−2220000
χ18222-2-2222-2-2-2-22002-200022-2-20000i2i2−i2−i200i2i2i2i2−i2−i2−i2−i200000000000000−2i2i22−2−20000
χ19222-2-22-2-222-2-22222-22-2-2-2-22222-2-200002-200000000000000000000000000002-200
χ20222-2-22-2-222-2-22222-22-2-2-2-22222-2-200002-20000000000000000000000000000-2200
χ21222-2-22-2-222-2-22-2-22-2-222-2-222-2-2220000-22000000000000002-222-2-2000000000000
χ22222-2-22-2-222-2-22-2-22-2-222-2-222-2-2220000-2200000000000000-22-2-222000000000000
χ23222-2-2-1-2-22211-1-2-2-11-22211-1-111-1-100001-1−i3−i3i3i3−i3−i3i3i300−i3−i3i3i32-2-1-111000000000000
χ24222-2-2-1-2-22211-1-2-2-11-22211-1-111-1-100001-1−i3−i3i3i3−i3−i3i3i300i3i3−i3−i3-2211-1-1000000000000
χ25222-2-2-1-2-22211-1-2-2-11-22211-1-111-1-100001-1i3i3−i3−i3i3i3−i3−i300−i3−i3i3i3-2211-1-1000000000000
χ26222-2-2-1-2-22211-1-2-2-11-22211-1-111-1-100001-1i3i3−i3−i3i3i3−i3−i300i3i3−i3−i32-2-1-111000000000000
χ2722-22-222-2-2222222-2-2-2-222-22-222220000-2-20000000000000000000000002-22-20000
χ2822-22-222-2-2222222-2-2-2-222-22-222220000-2-2000000000000000000000000-22-220000
χ2922-22-222-2-22222-2-2-2-222-22-22-2-2-2-2-22i−2i2i−2i222i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ3022-22-222-2-22222-2-2-2-222-22-22-2-2-2-2-2−2i2i−2i2i22−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ3122-22-2-12-2-22-1-1-1-2-21122-2-11-1111112i−2i2i−2i-1-1−ii−ii−ii−ii00−i3i3−i3i3003−33−3000000000000
χ3222-22-2-12-2-22-1-1-1-2-21122-2-11-1111112i−2i2i−2i-1-1−ii−ii−ii−ii00i3−i3i3−i300−33−33000000000000
χ3322-22-2-12-2-22-1-1-1-2-21122-2-11-111111−2i2i−2i2i-1-1i−ii−ii−ii−i00−i3i3−i3i300−33−33000000000000
χ3422-22-2-12-2-22-1-1-1-2-21122-2-11-111111−2i2i−2i2i-1-1i−ii−ii−ii−i00i3−i3i3−i3003−33−3000000000000
χ3522-2-2222-22-2-2-2200-220002-2-2200002−2−22002−22−2−22−220000000000002-2002−2−220000
χ3622-2-2222-22-2-2-2200-220002-2-2200002−2−22002−22−2−22−22000000000000-2200−222−20000
χ3722-2-2222-22-2-2-2200-220002-2-220000−222−200−22−222−22−20000000000002-200−222−20000
χ3822-2-2222-22-2-2-2200-220002-2-220000−222−200−22−222−22−2000000000000-22002−2−220000
χ3922-2-222-22-22-2-2222-22-22-2-222-222-2-20000-22000000002-22-2-22000000000000000000
χ4022-2-222-22-22-2-2222-22-22-2-222-222-2-20000-2200000000-22-222-2000000000000000000
χ4122-2-222-22-22-2-22-2-2-222-22-222-2-2-22200002-20000000000000000000000000000002-2
χ4222-2-222-22-22-2-22-2-2-222-22-222-2-2-22200002-2000000000000000000000000000000-22
χ4322-2-22-1-22-2211-1221-1-22-21-1-11-1-11100001-13−3−333−3−332-2-111-1003−3−33000000000000
χ4422-2-22-1-22-2211-1221-1-22-21-1-11-1-11100001-13−3−333−3−33-221-1-1100−333−3000000000000
χ4522-2-22-1-22-2211-1221-1-22-21-1-11-1-11100001-1−333−3−333−32-2-111-100−333−3000000000000
χ4622-2-22-1-22-2211-1221-1-22-21-1-11-1-11100001-1−333−3−333−3-221-1-11003−3−33000000000000
χ47444444-4-4-4-44440044000-4-4-4-4000000000000000000000000000000000000000000
χ4844444-24444-2-2-2-4-4-2-2-4-4-4-2-2-2-2222200002200000000000000000000000000000000
χ4944444-2-4-4-4-4-2-2-200-2-20002222000000000066−6−6−6−666000000000000000000000000
χ5044444-2-4-4-4-4-2-2-200-2-200022220000000000−6−66666−6−6000000000000000000000000
χ51444-4-4-244-4-422-200-22000-2-2220000−2i2−2i22i22i200i2i2i2i2−i2−i2−i2−i2000000000000000000000000
χ52444-4-4-244-4-422-200-22000-2-22200002i22i2−2i2−2i200−i2−i2−i2−i2i2i2i2i2000000000000000000000000
χ53444-4-4-2-4-44422-244-224-4-422-2-2-2-2220000-2200000000000000000000000000000000
χ5444-44-44-444-444400-4-4000-44-44000000000000000000000000000000000000000000
χ5544-44-4-24-4-44-2-2-24422-4-44-22-22-2-2-2-200002200000000000000000000000000000000
χ5644-44-4-2-444-4-2-2-200220002-22-20000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ5744-44-4-2-444-4-2-2-200220002-22-20000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ5844-4-44-24-44-422-2002-2000-222-2000022−22−222200−22−222−22−2000000000000000000000000
χ5944-4-44-24-44-422-2002-2000-222-20000−222222−22002−22−2−22−22000000000000000000000000
χ6044-4-44-2-44-4422-2-4-42-24-442-2-2222-2-20000-2200000000000000000000000000000000
χ618-80008000000-842−4200000000042−420000000000000000000000000000000000000000
χ628-80008000000-8−4242000000000−42420000000000000000000000000000000000000000
χ638-8000-40000−4i34i3442−42000000000−22222i6−2i600000000000000000000000000000000000000
χ648-8000-40000−4i34i34−424200000000022−22−2i62i600000000000000000000000000000000000000
χ658-8000-400004i3−4i3442−42000000000−2222−2i62i600000000000000000000000000000000000000
χ668-8000-400004i3−4i34−424200000000022−222i6−2i600000000000000000000000000000000000000

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