Finite Group Databasebeta

← Group #10786607

Character table — Group #10786607

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111222222222222444444444444444448888888888888888888812121212121212121212161616161616161624242448484848
order12223444466688884448812121212121212122424242424444668812121212122424242424242288888888441212121212124884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11-1-1-1-111-1-11111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1
χ4111111111111111111111111111111111-1-11-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-111111-1-1-1-111111111-11111-1-1111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-1
χ61111111111111111-1-111111-1-1-1-111111111-11111-1-1111-1-111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-111
χ71111111111111111-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111111-1-111
χ81111111111111111-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-11111111111-1-11111-1-1-111-1-1
χ9111111111111-1-1-1-1111-1-111111111-1-1-1-11-111-111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-11-11-111-1-11-1-11-11-1
χ10111111111111-1-1-1-1111-1-111111111-1-1-1-11-111-111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111-11-111-1-1-111-11-11
χ11111111111111-1-1-1-1111-1-111111111-1-1-1-1-111-11-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-1-11-11-1-1111-1-1-11-11
χ12111111111111-1-1-1-1111-1-111111111-1-1-1-1-111-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-1-111-1111-11-1
χ13111111111111-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-11-1-11-11111-1-11-1-1-1-1111111-1-1-1-11111-111-1-1-1111-1-11-1-11
χ14111111111111-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-11-1-11-11111-1-11-1-1-1-11111-1-11111-1-1-1-1-111-1-1-111-111-111-1
χ15111111111111-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-1-11-1-11-1-111111-1-1-1-1111111-1-1-1-111111-1-1111-1-11-1-1-111-1
χ16111111111111-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-1-11-1-11-1-111111-1-1-1-11111-1-11111-1-1-1-11-1-1111-1-1-1111-1-11
χ172222222-2-2222222200-2-2-2-2-20000222222220-2-2220022-200-2-20000000000000000-2-200000000000
χ182222222-2-2222222200-2-2-2-2-20000222222-2-2022-2-200-2-2-200-2-200000000000000002200000000000
χ192222222-2-2222-2-2-2-200-222-2-2000022-2-2-2-22-20-222200-2-2-200220000000000000000-2200000000000
χ202222222-2-2222-2-2-2-200-222-2-2000022-2-2-2-2-2202-2-2-20022-2002200000000000000002-200000000000
χ2122222-2-222222000022-200222222-2-2000000-200000000-2-2-20000002222-2-2000000000000-2000000
χ2222222-2-222222000022-200222222-2-2000000-200000000-2-2-2000000-2-2-2-2220000000000002000000
χ2322222-2-2222220000-2-2-20022-2-2-2-2-2-2000000200000000-22200000022-2-222000000000000-2000000
χ2422222-2-2222220000-2-2-20022-2-2-2-2-2-2000000200000000-222000000-2-222-2-20000000000002000000
χ252222-12222-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-122222-1-122-1-1-1-1-1-1-1-1-1-1-1000000000022-1-1-1-1-1-10000000
χ262222-12222-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-2-22-2-2112211-1-1-1-1-1-1-1-1-10000000000-2-21111110000000
χ272222-12222-1-1-12222-2-2222-1-11111-1-1-1-1-1-122-222-1-1-2-2-1-1-111-1-111110000000000-2-2-1-111110000000
χ282222-12222-1-1-12222-2-2222-1-11111-1-1-1-1-1-1-2-2-2-2-211-2-211-111-1-1111100000000002211-1-1-1-10000000
χ292222-12222-1-1-1-2-2-2-2222-2-2-1-1-1-1-1-1-1-111112-222-2-1-1-2-211-1-1-111111100000000002-2-11-1-1110000000
χ302222-12222-1-1-1-2-2-2-2222-2-2-1-1-1-1-1-1-1-11111-222-2211-2-2-1-1-1-1-11111110000000000-221-111-1-10000000
χ312222-12222-1-1-1-2-2-2-2-2-22-2-2-1-11111-1-111112-2-22-2-1-12211-11111-1-1-1-10000000000-22-1111-1-10000000
χ322222-12222-1-1-1-2-2-2-2-2-22-2-2-1-11111-1-11111-22-2-221122-1-1-11111-1-1-1-100000000002-21-1-1-1110000000
χ332222-122-2-2-1-1-1222200-2-2-211−i3−i3i3i3-1-1-1-1-1-1220-2-2-1-100-1-11−i3i311−i3−i3i3i300000000000011−i3i3−i3i30000000
χ342222-122-2-2-1-1-1222200-2-2-211−i3−i3i3i3-1-1-1-1-1-1-2-20221100111−i3i311−i3−i3i3i3000000000000-1-1i3−i3i3−i30000000
χ352222-122-2-2-1-1-1222200-2-2-211i3i3−i3−i3-1-1-1-1-1-1220-2-2-1-100-1-11i3−i311i3i3−i3−i300000000000011i3−i3i3−i30000000
χ362222-122-2-2-1-1-1222200-2-2-211i3i3−i3−i3-1-1-1-1-1-1-2-20221100111i3−i311i3i3−i3−i3000000000000-1-1−i3i3−i3i30000000
χ372222-122-2-2-1-1-1-2-2-2-200-22211−i3−i3i3i3-1-111112-20-22-1-100111−i3i3-1-1i3i3−i3−i30000000000001-1−i3i3i3−i30000000
χ382222-122-2-2-1-1-1-2-2-2-200-22211−i3−i3i3i3-1-11111-2202-21100-1-11−i3i3-1-1i3i3−i3−i3000000000000-11i3−i3−i3i30000000
χ392222-122-2-2-1-1-1-2-2-2-200-22211i3i3−i3−i3-1-111112-20-22-1-100111i3−i3-1-1−i3−i3i3i30000000000001-1i3−i3−i3i30000000
χ402222-122-2-2-1-1-1-2-2-2-200-22211i3i3−i3−i3-1-11111-2202-21100-1-11i3−i3-1-1−i3−i3i3i3000000000000-11−i3i3i3−i30000000
χ412-22-22002-2-22-2−i2−i2i2i22-20−i2i22-22-22-200−i2−i2i2i20000000−i2i200000−i2i2−i2i2−i2i22-22-200−i2−i2i2i2000000000−i2i20000
χ422-22-22002-2-22-2−i2−i2i2i22-20−i2i22-22-22-200−i2−i2i2i20000000−i2i200000−i2i2−i2i2−i2i2-22-2200i2i2−i2−i2000000000i2−i20000
χ432-22-22002-2-22-2−i2−i2i2i2-220−i2i22-2-22-2200−i2−i2i2i20000000i2−i200000−i2i2i2−i2i2−i22-2-2200i2i2−i2−i2000000000−i2i20000
χ442-22-22002-2-22-2−i2−i2i2i2-220−i2i22-2-22-2200−i2−i2i2i20000000i2−i200000−i2i2i2−i2i2−i2-222-200−i2−i2i2i2000000000i2−i20000
χ452-22-22002-2-22-2i2i2−i2−i22-20i2−i22-22-22-200i2i2−i2−i20000000i2−i200000i2−i2i2−i2i2−i22-22-200i2i2−i2−i2000000000i2−i20000
χ462-22-22002-2-22-2i2i2−i2−i22-20i2−i22-22-22-200i2i2−i2−i20000000i2−i200000i2−i2i2−i2i2−i2-22-2200−i2−i2i2i2000000000−i2i20000
χ472-22-22002-2-22-2i2i2−i2−i2-220i2−i22-2-22-2200i2i2−i2−i20000000−i2i200000i2−i2−i2i2−i2i22-2-2200−i2−i2i2i2000000000i2−i20000
χ482-22-22002-2-22-2i2i2−i2−i2-220i2−i22-2-22-2200i2i2−i2−i20000000−i2i200000i2−i2−i2i2−i2i2-222-200i2i2−i2−i2000000000−i2i20000
χ4944444-4-4-4-4444000000400-4-40000-4-40000000000000004000000000000000000000000000000000
χ504444-2-4-444-2-2-2000044-400-2-2-2-2-2-222000000-4000000002220000000000000000000000000000000
χ514444-2-4-444-2-2-20000-4-4-400-2-22222220000004000000002-2-20000000000000000000000000000000
χ524444-2-4-4-4-4-2-2-200000040022−2i3−2i32i32i322000000000000000-22i3−2i30000000000000000000000000000000
χ534444-2-4-4-4-4-2-2-2000000400222i32i3−2i3−2i322000000000000000-2−2i32i30000000000000000000000000000000
χ5444-4-444-4004-4-4000000000000000-4400000000000000000000000000000022−2222−22000000000000000
χ5544-4-444-4004-4-4000000000000000-44000000000000000000000000000000−2222−2222000000000000000
χ5644-4-44-44004-4-44-44-4000000000004-44-44-4000000000000000000000000000000000000000000000
χ5744-4-44-44004-4-4-44-44000000000004-4-44-44000000000000000000000000000000000000000000000
χ5844-4-4-2-4400-2224-44-400000000000-22-22-2200000−2i32i300−2i32i30000000000000000000000000000000000
χ5944-4-4-2-4400-2224-44-400000000000-22-22-22000002i3−2i3002i3−2i30000000000000000000000000000000000
χ6044-4-4-2-4400-222-44-4400000000000-222-22-200000−2i32i3002i3−2i30000000000000000000000000000000000
χ6144-4-4-2-4400-222-44-4400000000000-222-22-2000002i3−2i300−2i32i30000000000000000000000000000000000
χ624-44-4400-44-44-4−2i2−2i22i22i20002i2−2i2-44000000−2i2−2i22i22i2000000000000002i2−2i200000000000000000000000000000
χ634-44-4400-44-44-42i22i2−2i2−2i2000−2i22i2-440000002i22i2−2i2−2i200000000000000−2i22i200000000000000000000000000000
χ644-44-4-2004-42-22−2i2−2i22i22i24-40−2i22i2-22-22-2200i2i2−i2−i20000000−2i22i200000i2−i2i2−i2i2−i20000000000000000000000000
χ654-44-4-2004-42-22−2i2−2i22i22i2-440−2i22i2-222-22-200i2i2−i2−i200000002i2−2i200000i2−i2−i2i2−i2i20000000000000000000000000
χ664-44-4-2004-42-222i22i2−2i2−2i24-402i2−2i2-22-22-2200−i2−i2i2i200000002i2−2i200000−i2i2−i2i2−i2i20000000000000000000000000
χ674-44-4-2004-42-222i22i2−2i2−2i2-4402i2−2i2-222-22-200−i2−i2i2i20000000−2i22i200000−i2i2i2−i2i2−i20000000000000000000000000
χ684-44-4-200-442-22−2i2−2i22i22i20002i2−2i22-2−2i32i32i3−2i300i2i2−i2−i200000000000000−i2i2−666−60000000000000000000000000
χ694-44-4-200-442-22−2i2−2i22i22i20002i2−2i22-22i3−2i3−2i32i300i2i2−i2−i200000000000000−i2i26−6−660000000000000000000000000
χ704-44-4-200-442-222i22i2−2i2−2i2000−2i22i22-2−2i32i32i3−2i300−i2−i2i2i200000000000000i2−i26−6−660000000000000000000000000
χ714-44-4-200-442-222i22i2−2i2−2i2000−2i22i22-22i3−2i3−2i32i300−i2−i2i2i200000000000000i2−i2−666−60000000000000000000000000
χ724-4-4440000-4-44−2i22i22i2−2i20000000000000−2i22i22i2−2i200000000000000000000000022−222i−2i−2i2i000000000000000
χ734-4-4440000-4-44−2i22i22i2−2i20000000000000−2i22i22i2−2i2000000000000000000000000−2222−2i2i2i−2i000000000000000
χ744-4-4440000-4-442i2−2i2−2i22i200000000000002i2−2i2−2i22i200000000000000000000000022−22−2i2i2i−2i000000000000000
χ754-4-4440000-4-442i2−2i2−2i22i200000000000002i2−2i2−2i22i2000000000000000000000000−22222i−2i−2i2i000000000000000
χ7688-8-8-48-800-4440000000000000004-40000000000000000000000000000000000000000000000000
χ778-8-88-4000044-4−4i24i24i2−4i200000000000002i2−2i2−2i22i2000000000000000000000000000000000000000000000
χ788-8-88-4000044-44i2−4i2−4i24i20000000000000−2i22i22i2−2i2000000000000000000000000000000000000000000000

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