Finite Group Databasebeta

← Group #10949655

Character table — Group #10949655

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222223333444444444444444444666666888888888888121212121212121212121212161616163232323248484848
order1222344666888844442488121216161616161616162424242422888861224244848484848484848248816161616161616164444121212122244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-11-11-11-1
χ4111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-11-11-11-11
χ5111111111111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11-11-111-1-1-1-111
χ6111111111111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-11111-1-1
χ7111111111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-111-1-11-111-1
χ8111111111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-111-11-1-11
χ911111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1011111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ1111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11-11-1-11-11
χ1211111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-11-111-11-1
χ1311111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-111-1-111-1-1
χ1411111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-11-11-1-111-1-111
χ1511111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-111-1-111-1-11
χ1611111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1-111-1-111-1
χ172222222222-2-2-2-2222222-2-22200000000-2-2-2-222-2-2-2-222-2-20000000022-2-200000000000000000000
χ182222222222-2-2-2-22222-2-2222200000000-2-2-2-222-2-2-2-2-2-22200000000-2-22200000000000000000000
χ192222222222-2-2-2-2-2-2-2-222-2-22200000000-2-2-2-2-2-2222222-2-200000000-2-22200000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2222200000000-2-2-2-2-2-22222-2-2220000000022-2-200000000000000000000
χ2122222-2-2222000022222-200-2-222−2−222−2−20000-2-200002-20022−2−222−2−2-220022−2−222−2−2000000000000
χ2222222-2-2222000022222-200-2-2−2−222−2−2220000-2-200002-200−2−222−2−222-2200−2−222−2−222000000000000
χ2322222-2-222200002222-2200-2-222−2−2−2−2220000-2-20000-220022−2−2−2−2222-20022−2−2−2−222000000000000
χ2422222-2-222200002222-2200-2-2−2−22222−2−20000-2-20000-2200−2−22222−2−22-200−2−22222−2−2000000000000
χ2522222-2-22220000-2-2-2-22-200-2-222−2−222−2−200002200002-20022−2−222−2−22-200−2−222−2−222000000000000
χ2622222-2-22220000-2-2-2-22-200-2-2−2−222−2−22200002200002-200−2−222−2−2222-20022−2−222−2−2000000000000
χ2722222-2-22220000-2-2-2-2-2200-2-222−2−2−2−2220000220000-220022−2−2−2−222-2200−2−22222−2−2000000000000
χ2822222-2-22220000-2-2-2-2-2200-2-2−2−22222−2−20000220000-2200−2−22222−2−2-220022−2−2−2−222000000000000
χ292222-122-1-1-1222200002222-1-122222222-1-1-1-1000000-1-1-1-1-1-1-1-1-1-1-1-10000000000002222-1-1-1-10000
χ302222-122-1-1-1222200002222-1-122222222-1-1-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-211110000
χ312222-122-1-1-1222200002222-1-1-2-2-2-2-2-2-2-2-1-1-1-1000000-1-1-1-11111111100000000000022-2-2-11-110000
χ322222-122-1-1-1222200002222-1-1-2-2-2-2-2-2-2-2-1-1-1-1000000-1-1-1-111111111000000000000-2-2221-11-10000
χ332222-122-1-1-122220000-2-2-2-2-1-12222-2-2-2-2-1-1-1-10000001111-1-1-1-111110000000000002-22-2-1-1110000
χ342222-122-1-1-122220000-2-2-2-2-1-12222-2-2-2-2-1-1-1-10000001111-1-1-1-11111000000000000-22-2211-1-10000
χ352222-122-1-1-122220000-2-2-2-2-1-1-2-2-2-22222-1-1-1-100000011111111-1-1-1-10000000000002-2-22-111-10000
χ362222-122-1-1-122220000-2-2-2-2-1-1-2-2-2-22222-1-1-1-100000011111111-1-1-1-1000000000000-222-21-1-110000
χ3722-2-222-2-2-22000022-2-2002i−2i2-22−22−2i2−i2i2−i200002-20000002i−2i2−22−2i2−i2i2−i2002i−2i2−22−2i2−i2i2−i2000000000000
χ3822-2-222-2-2-22000022-2-2002i−2i2-2−22−22−i2i2−i2i200002-20000002i−2i−22−22−i2i2−i2i2002i−2i−22−22−i2i2−i2i2000000000000
χ3922-2-222-2-2-22000022-2-200−2i2i2-22−22−2−i2i2−i2i200002-2000000−2i2i2−22−2−i2i2−i2i200−2i2i2−22−2−i2i2−i2i2000000000000
χ4022-2-222-2-2-22000022-2-200−2i2i2-2−22−22i2−i2i2−i200002-2000000−2i2i−22−22i2−i2i2−i200−2i2i−22−22i2−i2i2−i2000000000000
χ4122-2-222-2-2-220000-2-222002i−2i2-22−22−2i2−i2i2−i20000-220000002i−2i2−22−2i2−i2i2−i200−2i2i−22−22−i2i2−i2i2000000000000
χ4222-2-222-2-2-220000-2-222002i−2i2-2−22−22−i2i2−i2i20000-220000002i−2i−22−22−i2i2−i2i200−2i2i2−22−2i2−i2i2−i2000000000000
χ4322-2-222-2-2-220000-2-22200−2i2i2-22−22−2−i2i2−i2i20000-22000000−2i2i2−22−2−i2i2−i2i2002i−2i−22−22i2−i2i2−i2000000000000
χ4422-2-222-2-2-220000-2-22200−2i2i2-2−22−22i2−i2i2−i20000-22000000−2i2i−22−22i2−i2i2−i2002i−2i2−22−2−i2i2−i2i2000000000000
χ4522-2-22-22-2-2222-2-222-2-20000-2200002i−2i−2i2i22-2-2-2222-2-2000000002i−2i−2i2i000000002i−2i−2i2i000000000000
χ4622-2-22-22-2-2222-2-222-2-20000-220000−2i2i2i−2i22-2-2-2222-2-200000000−2i2i2i−2i00000000−2i2i2i−2i000000000000
χ4722-2-22-22-2-2222-2-2-2-2220000-2200002i−2i−2i2i22-2-22-2-2-222000000002i−2i−2i2i00000000−2i2i2i−2i000000000000
χ4822-2-22-22-2-2222-2-2-2-2220000-220000−2i2i2i−2i22-2-22-2-2-22200000000−2i2i2i−2i000000002i−2i−2i2i000000000000
χ4922-2-22-22-2-22-2-22222-2-20000-222-2-220000-2-222-22-2-22200002-2-22000000002-2-220000000000000000
χ5022-2-22-22-2-22-2-22222-2-20000-22-222-20000-2-222-22-2-2220000-222-200000000-222-20000000000000000
χ5122-2-22-22-2-22-2-222-2-2220000-222-2-220000-2-2222-222-2-200002-2-2200000000-222-20000000000000000
χ5222-2-22-22-2-22-2-222-2-2220000-22-222-20000-2-2222-222-2-20000-222-2000000002-2-220000000000000000
χ534444-244-2-2-2-4-4-4-4000044-4-4-2-2000000002222000000-2-22200000000000000000000000000000000
χ544444-244-2-2-2-4-4-4-40000-4-444-2-200000000222200000022-2-200000000000000000000000000000000
χ554444-2-4-4-2-2-2000000004-400222222−22−222222−22−220000000000-2200−2−222−2−222000000000000000000000000
χ564444-2-4-4-2-2-2000000004-40022−22−222222−22−2222220000000000-220022−2−222−2−2000000000000000000000000
χ574444-2-4-4-2-2-200000000-4400222222−22−22−22−22222200000000002-200−2−22222−2−2000000000000000000000000
χ584444-2-4-4-2-2-200000000-440022−22−2222222222−22−2200000000002-20022−2−2−2−222000000000000000000000000
χ5944-4-4-24-422-200000000004i−4i-2222−2222−222i2−2i22i2−2i2000000000000−2i2i−22−22−i2i2−i2i2000000000000000000000000
χ6044-4-4-24-422-200000000004i−4i-22−2222−2222−2i22i2−2i22i2000000000000−2i2i2−22−2i2−i2i2−i2000000000000000000000000
χ6144-4-4-24-422-20000000000−4i4i-2222−2222−22−2i22i2−2i22i20000000000002i−2i−22−22i2−i2i2−i2000000000000000000000000
χ6244-4-4-24-422-20000000000−4i4i-22−2222−22222i2−2i22i2−2i20000000000002i−2i2−22−2−i2i2−i2i2000000000000000000000000
χ6344-4-4-2-4422-244-4-4000000002-200004i−4i−4i4i-2-22200000000000000−2i2i2i−2i000000000000000000000000
χ6444-4-4-2-4422-244-4-4000000002-20000−4i4i4i−4i-2-222000000000000002i−2i−2i2i000000000000000000000000
χ6544-4-4-2-4422-2-4-444000000002-24-4-44000022-2-20000000000-222-20000000000000000000000000000
χ6644-4-4-2-4422-2-4-444000000002-2-444-4000022-2-200000000002-2-220000000000000000000000000000
χ674-44-44004-4-422−2222−224i−4i4i−4i0000000000000022−2222−22002i2−2i22i2−2i2000000000000000000000000000000000000
χ684-44-44004-4-422−2222−22−4i4i−4i4i0000000000000022−2222−2200−2i22i2−2i22i2000000000000000000000000000000000000
χ694-44-44004-4-4−2222−22224i−4i4i−4i00000000000000−2222−222200−2i22i2−2i22i2000000000000000000000000000000000000
χ704-44-44004-4-4−2222−2222−4i4i−4i4i00000000000000−2222−2222002i2−2i22i2−2i2000000000000000000000000000000000000
χ714-4-44400-44-422−22−22224i−4i−4i4i0000000000000022−22−2222002i2−2i2−2i22i2000000000000000000000000000000000000
χ724-4-44400-44-422−22−2222−4i4i4i−4i0000000000000022−22−222200−2i22i22i2−2i2000000000000000000000000000000000000
χ734-4-44400-44-4−222222−224i−4i−4i4i00000000000000−222222−2200−2i22i22i2−2i2000000000000000000000000000000000000
χ744-4-44400-44-4−222222−22−4i4i4i−4i00000000000000−222222−22002i2−2i2−2i22i2000000000000000000000000000000000000
χ758-88-8-400-44442−4242−42000000000000000000−2222−2222000000000000000000000000000000000000000000
χ768-88-8-400-444−4242−424200000000000000000022−2222−22000000000000000000000000000000000000000000
χ778-8-88-4004-4442−42−4242000000000000000000−222222−22000000000000000000000000000000000000000000
χ788-8-88-4004-44−424242−4200000000000000000022−22−2222000000000000000000000000000000000000000000

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