Finite Group Databasebeta

← Group #10858717

Character table — Group #10858717

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222444444444444444444444444444488888888888888888888888888888881212242424242424242424484848
order12222234444666224444446688121212121212121212121212242424242244446666668881212121212121212121224242424242488444444888488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1111111111111-1-1-1-1-1-1-111-111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1111-1-1-1
χ4111111111111111111111111-1-1111111111111-1-1-1-1-1-1-111-111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111
χ5111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11-1-1111-1-1-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1-1-111111-1-11
χ6111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11-1-1111-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-111-1
χ7111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-1
χ8111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-11
χ911111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1111111111-1-11111-1-1-11-1
χ1011111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1111-11
χ1111111111111111-1-1-1-1111111-1-1111111111111-1-1-1-1111-1-11-1-11111-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1111-1-11-1-11-1-11-11
χ1211111111111111-1-1-1-1111111-1-1111111111111-1-1-1-1111-1-11-1-11111-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-111-111-111-11-1
χ1311111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-11-1-1-1-11111-1-111-1-1-1-111-111-1111-1-11-1-1
χ1411111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-11-1-1-1-11111-1-111-1-1-1-1-1-11-1-11-1-1-111-111
χ1511111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-111111111-1-1111111-111-1-1-11-1-1-111
χ1611111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-111111111-1-11111-1-11-1-1111-1111-1-1
χ17222222-12222-1-1-122222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ18222222-12222-1-1-122222222-1-1-2-2-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-222-2-1-11111-2-2-2-1-111-1-1-1-11111111100000000000000
χ19222222-12222-1-1-12222-2-2-2-2-1-122-1-111111111-1-1-1-1-1-1-2-22-2-22-1-11111-2-22-1-1-1-11111-1-1-1-1111100000000000000
χ20222222-12222-1-1-12222-2-2-2-2-1-1-2-2-1-111111111-1-1111122-2-2-2-2-1-1-1-1-1-122-2-1-11111111111-1-1-1-100000000000000
χ21222222-12222-1-1-1-2-2-2-22222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111112221111111111-1-1-1-1-1-100000000000000
χ22222222-12222-1-1-1-2-2-2-22222-1-1-2-2-1-1-1-1-1-1-1-1-1-1-1-11111222-2-2211-1-1-1-1-2-2-211-1-11111-1-111111100000000000000
χ23222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-122-1-111111111-1-1-1-1-1-122-222-211-1-1-1-1-2-221111-1-1-1-111-1-1111100000000000000
χ24222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-2-2-1-111111111-1-11111-2-2222211111122-211-1-1-1-1-1-1-1-111-1-1-1-100000000000000
χ252222-2-222-2-22222000022-2-2-2-200222222-2-2-2-2-2-20000000000000000000000000000000000022-200200-200000
χ262222-2-222-2-22222000022-2-2-2-200222222-2-2-2-2-2-200000000000000000000000000000000000-2-2200-200200000
χ272222-2-222-2-222220000-2-222-2-20022-2-2-2-22222-2-20000000000000000000000000000000000022200-200-200000
χ282222-2-222-2-222220000-2-222-2-20022-2-2-2-22222-2-200000000000000000000000000000000000-2-2-200200200000
χ292222-2-22-222-222222-2-20000-2-222-2-20000000022222200-200222000000-2-2-2-2-2000022-2-2000000000000000000
χ302222-2-22-222-222222-2-20000-2-2-2-2-2-20000000022-2-2-2-200200-2220000002-2-2220000-2-222000000000000000000
χ312222-2-22-222-2222-2-2220000-2-222-2-20000000022222200200-2-2-2000000-222220000-2-2-2-2000000000000000000
χ322222-2-22-222-2222-2-2220000-2-2-2-2-2-20000000022-2-2-2-200-2002-2-2000000222-2-200002222000000000000000000
χ332222-2-2-1-222-2-1-1-122-2-20000112211−i3−i3i3i3−i3−i3i3i3-1-1-1-1-1-100-2002-1-1−i3−i3i3i300-21111−i3−i3i3i3-1-111−i3−i3i3i300000000000000
χ342222-2-2-1-222-2-1-1-122-2-20000112211i3i3−i3−i3i3i3−i3−i3-1-1-1-1-1-100-2002-1-1i3i3−i3−i300-21111i3i3−i3−i3-1-111i3i3−i3−i300000000000000
χ352222-2-2-1-222-2-1-1-122-2-2000011-2-211−i3−i3i3i3−i3−i3i3i3-1-1111100200-2-1-1i3i3−i3−i300211-1-1−i3−i3i3i311-1-1i3i3−i3−i300000000000000
χ362222-2-2-1-222-2-1-1-122-2-2000011-2-211i3i3−i3−i3i3i3−i3−i3-1-1111100200-2-1-1−i3−i3i3i300211-1-1i3i3−i3−i311-1-1−i3−i3i3i300000000000000
χ372222-2-2-1-222-2-1-1-1-2-2220000112211−i3−i3i3i3−i3−i3i3i3-1-1-1-1-1-100200-211i3i3−i3−i300-2-1-1-1-1i3i3−i3−i31111−i3−i3i3i300000000000000
χ382222-2-2-1-222-2-1-1-1-2-2220000112211i3i3−i3−i3i3i3−i3−i3-1-1-1-1-1-100200-211−i3−i3i3i300-2-1-1-1-1−i3−i3i3i31111i3i3−i3−i300000000000000
χ392222-2-2-1-222-2-1-1-1-2-222000011-2-211−i3−i3i3i3−i3−i3i3i3-1-1111100-200211−i3−i3i3i3002-1-111i3i3−i3−i3-1-1-1-1i3i3−i3−i300000000000000
χ402222-2-2-1-222-2-1-1-1-2-222000011-2-211i3i3−i3−i3i3i3−i3−i3-1-1111100-200211i3i3−i3−i3002-1-111−i3−i3i3i3-1-1-1-1−i3−i3i3i300000000000000
χ4122-2-22-2222-2-22-2-22-22-200002-2002-2000000002-200002-200002-22-22-22-202-200000000002-22-200000000000000
χ4222-2-22-2222-2-22-2-22-22-200002-2002-2000000002-20000-2200002-2-22-22-2202-20000000000-22-2200000000000000
χ4322-2-22-2222-2-22-2-2-22-2200002-2002-2000000002-200002-20000-222-22-2-220-220000000000-22-2200000000000000
χ4422-2-22-2222-2-22-2-2-22-2200002-2002-2000000002-20000-220000-22-22-222-20-2200000000002-22-200000000000000
χ4522-2-22-22-2-2222-2-200002i−2i2i−2i2-200-222i−2i2i−2i2i−2i2i−2i-22000000000000000000000000000000000000002i−2i00002-2000
χ4622-2-22-22-2-2222-2-200002i−2i2i−2i2-200-222i−2i2i−2i2i−2i2i−2i-2200000000000000000000000000000000000000−2i2i0000-22000
χ4722-2-22-22-2-2222-2-20000−2i2i−2i2i2-200-22−2i2i−2i2i−2i2i−2i2i-22000000000000000000000000000000000000002i−2i0000-22000
χ4822-2-22-22-2-2222-2-20000−2i2i−2i2i2-200-22−2i2i−2i2i−2i2i−2i2i-2200000000000000000000000000000000000000−2i2i00002-2000
χ4922-2-22-2-122-2-2-1112-22-20000-1100-113−3−33−333−3-1133−3−32-20000-11-11-112-20-113−33−33−33−33−3-11-1100000000000000
χ5022-2-22-2-122-2-2-1112-22-20000-1100-113−3−33−333−3-11−3−333-220000-111-11-1-220-11−333−33−3−33−331-11-100000000000000
χ5122-2-22-2-122-2-2-1112-22-20000-1100-11−333−33−3−33-1133−3−3-220000-111-11-1-220-113−3−33−333−33−31-11-100000000000000
χ5222-2-22-2-122-2-2-1112-22-20000-1100-11−333−33−3−33-11−3−3332-20000-11-11-112-20-11−33−33−33−33−33-11-1100000000000000
χ5322-2-22-2-122-2-2-111-22-220000-1100-113−3−33−333−3-1133−3−3-2200001-11-11-12-201-1−33−33−33−333−3-11-1100000000000000
χ5422-2-22-2-122-2-2-111-22-220000-1100-113−3−33−333−3-11−3−3332-200001-1-11-11-2201-13−3−33−333−3−331-11-100000000000000
χ5522-2-22-2-122-2-2-111-22-220000-1100-11−333−33−3−33-1133−3−32-200001-1-11-11-2201-1−333−33−3−333−31-11-100000000000000
χ5622-2-22-2-122-2-2-111-22-220000-1100-11−333−33−3−33-11−3−333-2200001-11-11-12-201-13−33−33−33−3−33-11-1100000000000000
χ5722-2-2-222-22-222-2-22-2-222i−2i−2i2i-2200-222i−2i2i−2i−2i2i−2i2i2-200000002i−2i02-20000000-22002i−2i−2i2i0000000000000000000000
χ5822-2-2-222-22-222-2-22-2-22−2i2i2i−2i-2200-22−2i2i−2i2i2i−2i2i−2i2-20000000−2i2i02-20000000-2200−2i2i2i−2i0000000000000000000000
χ5922-2-2-222-22-222-2-2-222-22i−2i−2i2i-2200-222i−2i2i−2i−2i2i−2i2i2-20000000−2i2i0-2200000002-200−2i2i2i−2i0000000000000000000000
χ6022-2-2-222-22-222-2-2-222-2−2i2i2i−2i-2200-22−2i2i−2i2i2i−2i2i−2i2-200000002i−2i0-2200000002-2002i−2i−2i2i0000000000000000000000
χ6122-2-2-22-1-22-22-1112-2-222i−2i−2i2i1-1001-1−ii−iii−ii−i-1133−3−30002i−2i0-11−i3i3i3−i30001-1−33−iii−i3−3−33−i3i3i3−i300000000000000
χ6222-2-2-22-1-22-22-1112-2-222i−2i−2i2i1-1001-1−ii−iii−ii−i-11−3−3330002i−2i0-11i3−i3−i3i30001-13−3−iii−i−333−3i3−i3−i3i300000000000000
χ6322-2-2-22-1-22-22-1112-2-22−2i2i2i−2i1-1001-1i−ii−i−ii−ii-1133−3−3000−2i2i0-11i3−i3−i3i30001-1−33i−i−ii3−3−33i3−i3−i3i300000000000000
χ6422-2-2-22-1-22-22-1112-2-22−2i2i2i−2i1-1001-1i−ii−i−ii−ii-11−3−333000−2i2i0-11−i3i3i3−i30001-13−3i−i−ii−333−3−i3i3i3−i300000000000000
χ6522-2-2-22-1-22-22-111-222-22i−2i−2i2i1-1001-1−ii−iii−ii−i-1133−3−3000−2i2i01-1i3−i3−i3i3000-113−3i−i−ii−33−33−i3i3i3−i300000000000000
χ6622-2-2-22-1-22-22-111-222-22i−2i−2i2i1-1001-1−ii−iii−ii−i-11−3−333000−2i2i01-1−i3i3i3−i3000-11−33i−i−ii3−33−3i3−i3−i3i300000000000000
χ6722-2-2-22-1-22-22-111-222-2−2i2i2i−2i1-1001-1i−ii−i−ii−ii-1133−3−30002i−2i01-1−i3i3i3−i3000-113−3−iii−i−33−33i3−i3−i3i300000000000000
χ6822-2-2-22-1-22-22-111-222-2−2i2i2i−2i1-1001-1i−ii−i−ii−ii-11−3−3330002i−2i01-1i3−i3−i3i3000-11−33−iii−i3−33−3−i3i3i3−i300000000000000
χ694444444-4-4-4-4444000000004400-4-400000000-4-40000000000000000000000000000000000000000000000000
χ70444444-2-4-4-4-4-2-2-200000000-2-20022−2i3−2i32i32i32i32i3−2i3−2i3220000000000000000000000000000000000000000000000000
χ71444444-2-4-4-4-4-2-2-200000000-2-200222i32i3−2i3−2i3−2i3−2i32i32i3220000000000000000000000000000000000000000000000000
χ724444-4-4-24-4-44-2-2-2000044-4-42200-2-2-2-2-2-22222220000000000000000000000000000000000000000000000000
χ734444-4-4-24-4-44-2-2-20000-4-4442200-2-22222-2-2-2-2220000000000000000000000000000000000000000000000000
χ7444-4-44-4-2-4-444-22200004i−4i4i−4i-22002-2−2i2i−2i2i−2i2i−2i2i2-20000000000000000000000000000000000000000000000000
χ7544-4-44-4-2-4-444-2220000−4i4i−4i4i-22002-22i−2i2i−2i2i−2i2i−2i2-20000000000000000000000000000000000000000000000000
χ7644-4-4-4444-44-44-4-400000000-44004-400000000-440000000000000000000000000000000000000000000000000
χ7744-4-4-44-24-44-4-222000000002-200-2223−23−232323−23−23232-20000000000000000000000000000000000000000000000000
χ7844-4-4-44-24-44-4-222000000002-200-22−232323−23−232323−232-20000000000000000000000000000000000000000000000000
χ794-44-40040000-44-40000000000−2i22i2000000000000−2i22i2−2i22i20000000000000000000000000000000−2i22i200002-2000000
χ804-44-40040000-44-40000000000−2i22i2000000000000−2i22i2−2i22i200000000000000000000000000000002i2−2i20000-22000000
χ814-44-40040000-44-400000000002i2−2i20000000000002i2−2i22i2−2i20000000000000000000000000000000−2i22i20000-22000000
χ824-44-40040000-44-400000000002i2−2i20000000000002i2−2i22i2−2i200000000000000000000000000000002i2−2i200002-2000000
χ838-88-800-400004-440000000000−4i24i20000000000002i2−2i22i2−2i2000000000000000000000000000000000000000000000
χ848-88-800-400004-4400000000004i2−4i2000000000000−2i22i2−2i22i2000000000000000000000000000000000000000000000
χ858-8-880080000-8-880000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8800-4000044-40000000000000000000000002i6−2i6−2i62i6000000000000000000000000000000000000000000000
χ878-8-8800-4000044-4000000000000000000000000−2i62i62i6−2i6000000000000000000000000000000000000000000000

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