Finite Group Databasebeta

← Group #10709894

Character table — Group #10709894

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444121212121212121212121212121212123232323232329696
order12223444444666888888888888888812121212121224242424242424242424242424242424242424242424242416161616161616161616161616161616441212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1111-1
χ922222222222222-2-2-2-2-2-2-2-22222-2-2-2-2222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ1022222222222222-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000
χ112222222-2-2-2-22222222-2-2-2-200000000-2-2-2-2222222-2-2-2-20000000000000000000000002222-2-2-2-200000000
χ122222222-2-2-2-22222222-2-2-2-200000000-2-2-2-2222222-2-2-2-2000000000000000000000000-2-2-2-2222200000000
χ132222222-2-2-2-2222-2-2-2-2222200000000-2-2-2-222-2-2-2-2222200000000000000002222-2-2-2-20000000000000000
χ142222222-2-2-2-2222-2-2-2-2222200000000-2-2-2-222-2-2-2-222220000000000000000-2-2-2-222220000000000000000
χ1522222-2-222-2-222200000000000022-2-222-2-2-2-200000000000000002222-2-2-2-222−2−222−2−222−2−222−2−200000000
χ1622222-2-222-2-222200000000000022-2-222-2-2-2-200000000000000002222-2-2-2-2−2−222−2−222−2−222−2−22200000000
χ1722222-2-222-2-2222000000000000-2-22222-2-2-2-20000000000000000-2-2-2-2222222−2−222−2−2−2−222−2−22200000000
χ1822222-2-222-2-2222000000000000-2-22222-2-2-2-20000000000000000-2-2-2-22222−2−222−2−22222−2−222−2−200000000
χ1922222-2-2-2-2222220000000022-2-20000-2-222-2-2000000002222-2-2-2-20000000022−2−2−2−22222−2−2−2−22200000000
χ2022222-2-2-2-2222220000000022-2-20000-2-222-2-2000000002222-2-2-2-200000000−2−22222−2−2−2−22222−2−200000000
χ2122222-2-2-2-22222200000000-2-2220000-2-222-2-200000000-2-2-2-222220000000022−2−2−2−222−2−22222−2−200000000
χ2222222-2-2-2-22222200000000-2-2220000-2-222-2-200000000-2-2-2-2222200000000−2−22222−2−222−2−2−2−22200000000
χ232222-1222222-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-100
χ242222-1222222-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2111100
χ252222-1222222-1-1-122222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000002-2-1-11100
χ262222-1222222-1-1-122222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2211-1-100
χ272222-1222222-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-2-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111000000000000000000−i3i3−i3i300
χ282222-1222222-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-2-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111000000000000000000i3−i3i3−i300
χ292222-1222222-1-1-1-2-2-2-2-2-2-2-2-2-2-2-22222-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1000000000000000000−i3i3i3−i300
χ302222-1222222-1-1-1-2-2-2-2-2-2-2-2-2-2-2-22222-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1000000000000000000i3−i3−i3i300
χ3122-2-222-20000-2-22000022-2-22−22−22−22−200002-2000022-2-222−2−222−2−222−2−222−2−200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i200000000
χ3222-2-222-20000-2-22000022-2-22−22−22−22−200002-2000022-2-222−2−222−2−222−2−222−2−20000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i200000000
χ3322-2-222-20000-2-22000022-2-2−22−22−22−2200002-2000022-2-2−2−222−2−222−2−222−2−22200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i200000000
χ3422-2-222-20000-2-22000022-2-2−22−22−22−2200002-2000022-2-2−2−222−2−222−2−222−2−2220000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i200000000
χ3522-2-222-20000-2-220000-2-2222−22−2−22−2200002-20000-2-22222−2−222−2−2−2−222−2−2222i−2i2i−2i0000−i2i2−i2i2i2−i2i2−i200000000
χ3622-2-222-20000-2-220000-2-2222−22−2−22−2200002-20000-2-22222−2−222−2−2−2−222−2−222−2i2i−2i2i0000i2−i2i2−i2−i2i2−i2i200000000
χ3722-2-222-20000-2-220000-2-222−22−222−22−200002-20000-2-222−2−222−2−22222−2−222−2−22i−2i2i−2i0000i2−i2i2−i2−i2i2−i2i200000000
χ3822-2-222-20000-2-220000-2-222−22−222−22−200002-20000-2-222−2−222−2−22222−2−222−2−2−2i2i−2i2i0000−i2i2−i2i2i2−i2i2−i200000000
χ3922-2-22-220000-2-2222-2-200002−2−222−2−220000-2222-2-2000022−2−2−2−22222−2−2−2−222−i2i2i2−i2−i2i2i2−i200002i−2i−2i2i00000000
χ4022-2-22-220000-2-2222-2-200002−2−222−2−220000-2222-2-2000022−2−2−2−22222−2−2−2−222i2−i2−i2i2i2−i2−i2i20000−2i2i2i−2i00000000
χ4122-2-22-220000-2-2222-2-20000−222−2−222−20000-2222-2-20000−2−22222−2−2−2−22222−2−2−i2i2i2−i2−i2i2i2−i20000−2i2i2i−2i00000000
χ4222-2-22-220000-2-2222-2-20000−222−2−222−20000-2222-2-20000−2−22222−2−2−2−22222−2−2i2−i2−i2i2i2−i2−i2i200002i−2i−2i2i00000000
χ4322-2-22-220000-2-22-2-22200002−2−22−222−20000-22-2-222000022−2−2−2−222−2−22222−2−2−i2i2i2−i2i2−i2−i2i22i−2i−2i2i000000000000
χ4422-2-22-220000-2-22-2-22200002−2−22−222−20000-22-2-222000022−2−2−2−222−2−22222−2−2i2−i2−i2i2−i2i2i2−i2−2i2i2i−2i000000000000
χ4522-2-22-220000-2-22-2-2220000−222−22−2−220000-22-2-2220000−2−22222−2−222−2−2−2−222−i2i2i2−i2i2−i2−i2i2−2i2i2i−2i000000000000
χ4622-2-22-220000-2-22-2-2220000−222−22−2−220000-22-2-2220000−2−22222−2−222−2−2−2−222i2−i2−i2i2−i2i2i2−i22i−2i−2i2i000000000000
χ474444-244-4-4-4-4-2-2-24444-4-4-4-4000000002222-2-2-2-2-2-222220000000000000000000000000000000000000000
χ484444-244-4-4-4-4-2-2-2-4-4-4-44444000000002222-2-22222-2-2-2-20000000000000000000000000000000000000000
χ494444-2-4-444-4-4-2-2-200000000000044-4-4-2-222220000000000000000-2-2-2-22222000000000000000000000000
χ504444-2-4-444-4-4-2-2-2000000000000-4-444-2-2222200000000000000002222-2-2-2-2000000000000000000000000
χ514444-2-4-4-4-444-2-2-20000000044-4-4000022-2-22200000000-2-2-2-2222200000000000000000000000000000000
χ524444-2-4-4-4-444-2-2-200000000-4-444000022-2-222000000002222-2-2-2-200000000000000000000000000000000
χ5344-4-4-24-4000022-2000044-4-422−2222−2222−2222−220000-220000-2-222−2−222−2−222−2−222−2−222000000000000000000000000
χ5444-4-4-24-4000022-2000044-4-4−2222−2222−2222−22220000-220000-2-22222−2−222−2−222−2−222−2−2000000000000000000000000
χ5544-4-4-24-4000022-20000-4-44422−2222−22−2222−22220000-22000022-2-2−2−222−2−22222−2−222−2−2000000000000000000000000
χ5644-4-4-24-4000022-20000-4-444−2222−222222−2222−220000-22000022-2-222−2−222−2−2−2−222−2−222000000000000000000000000
χ5744-4-4-2-44000022-244-4-4000022−22−222222−22−222200002-2-2-2220000−2−22222−2−2−2−22222−2−2000000000000000000000000
χ5844-4-4-2-44000022-244-4-40000−222222−22−222222−2200002-2-2-222000022−2−2−2−22222−2−2−2−222000000000000000000000000
χ5944-4-4-2-44000022-2-4-444000022−22−2222−222222−2200002-222-2-20000−2−22222−2−222−2−2−2−222000000000000000000000000
χ6044-4-4-2-44000022-2-4-4440000−222222−2222−22−222200002-222-2-2000022−2−2−2−222−2−22222−2−2000000000000000000000000
χ614-44-4400004-44-4-422−2222−2222−2222−2200000000004-40022−2222−2222−2222−220000000000000000000000000000000000000000
χ624-44-4400004-44-4-4−2222−2222−2222−222200000000004-400−2222−2222−2222−22220000000000000000000000000000000000000000
χ634-44-440000-444-4-422−2222−22−2222−22220000000000-440022−2222−22−2222−22220000000000000000000000000000000000000000
χ644-44-440000-444-4-4−2222−222222−2222−220000000000-4400−2222−222222−2222−220000000000000000000000000000000000000000
χ654-44-4-200004-4-22222−2222−2222−2222−220000000000-2200−22−22−22−22−2i32i3−2i32i30000i6−i6i6−i6i6−i6i6−i6000000000000000000000000
χ664-44-4-200004-4-22222−2222−2222−2222−220000000000-2200−22−22−22−222i3−2i32i3−2i30000−i6i6−i6i6−i6i6−i6i6000000000000000000000000
χ674-44-4-200004-4-222−2222−2222−2222−22220000000000-22002−22−22−22−2−2i32i3−2i32i30000−i6i6−i6i6−i6i6−i6i6000000000000000000000000
χ684-44-4-200004-4-222−2222−2222−2222−22220000000000-22002−22−22−22−22i3−2i32i3−2i30000i6−i6i6−i6i6−i6i6−i6000000000000000000000000
χ694-44-4-20000-44-22222−2222−22−2222−222200000000002-200−22−222−22−20000−2i32i3−2i32i3i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ704-44-4-20000-44-22222−2222−22−2222−222200000000002-200−22−222−22−200002i3−2i32i3−2i3−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ714-44-4-20000-44-222−2222−222222−2222−2200000000002-2002−22−2−22−220000−2i32i3−2i32i3−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ724-44-4-20000-44-222−2222−222222−2222−2200000000002-2002−22−2−22−2200002i3−2i32i3−2i3i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ734-4-444004-400-44-422−22−222222−22−2222000000004-4000022−22−222222−22−22220000000000000000000000000000000000000000
χ744-4-444004-400-44-4−222222−22−222222−22000000004-40000−222222−22−222222−220000000000000000000000000000000000000000
χ754-4-44400-4400-44-422−22−2222−222222−2200000000-44000022−22−2222−222222−220000000000000000000000000000000000000000
χ764-4-44400-4400-44-4−222222−2222−22−222200000000-440000−222222−2222−22−22220000000000000000000000000000000000000000
χ774-4-44-2004-4002-2222−22−222222−22−222200000000-220000−222−2−222−2i6−i6−i6i6−i6i6i6−i6−2i32i32i3−2i30000000000000000000000000000
χ784-4-44-2004-4002-2222−22−222222−22−222200000000-220000−222−2−222−2−i6i6i6−i6i6−i6−i6i62i3−2i3−2i32i30000000000000000000000000000
χ794-4-44-2004-4002-22−222222−22−222222−2200000000-2200002−2−222−2−22i6−i6−i6i6−i6i6i6−i62i3−2i3−2i32i30000000000000000000000000000
χ804-4-44-2004-4002-22−222222−22−222222−2200000000-2200002−2−222−2−22−i6i6i6−i6i6−i6−i6i6−2i32i32i3−2i30000000000000000000000000000
χ814-4-44-200-44002-2222−22−2222−222222−22000000002-20000−222−22−2−22i6−i6−i6i6i6−i6−i6i600002i3−2i3−2i32i3000000000000000000000000
χ824-4-44-200-44002-2222−22−2222−222222−22000000002-20000−222−22−2−22−i6i6i6−i6−i6i6i6−i60000−2i32i32i3−2i3000000000000000000000000
χ834-4-44-200-44002-22−222222−2222−22−2222000000002-200002−2−22−222−2i6−i6−i6i6i6−i6−i6i60000−2i32i32i3−2i3000000000000000000000000
χ844-4-44-200-44002-22−222222−2222−22−2222000000002-200002−2−22−222−2−i6i6i6−i6−i6i6i6−i600002i3−2i3−2i32i3000000000000000000000000

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