Finite Group Databasebeta

← Group #10858723

Character table — Group #10858723

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222444444444444444444444444444488888888888888888888888888888881212242424242424242424484848
order1222223444466622444444666666881212121212121212242424244444448881212121212121212121212121212121224242424242488224444888488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-111111111-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1-1
χ41111111111111111111111111111-1-111111111-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111
χ5111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11-11-1
χ6111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-11-11
χ7111111111111111111-1-1-1-1111111-1-111111111-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-111-11
χ8111111111111111111-1-1-1-1111111-1-111111111-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-11-1
χ911111111111111-1-1-1-1111111-1-1-1-111111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-111111-1-11
χ1011111111111111-1-1-1-1111111-1-1-1-111111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-111-1
χ1111111111111111-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-11-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-111111-1
χ1211111111111111-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-11-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1111111-1-1-1-1-11
χ1311111111111111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-111111-11111-11-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-111-1-111-1-1
χ1411111111111111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-111111-11111-11-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111
χ1511111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1-11-1-1-1-11-1-1111-111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-11-111
χ1611111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1-11-1-1-1-11-1-1111-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1111111-11-1-1
χ17222222-12222-1-1-122222222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ18222222-12222-1-1-122222222-1-1-1-1-1-1-2-2-1-1-1-1-1-1-1-11111-2-2-222-2-2-2-2-1-1-1-1-1-1-1-11111111111111100000000000000
χ19222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-22221111111111111111-1-1-1-1-1-100000000000000
χ20222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-1-2-2-1-1-1-1-1-1-1-11111222-2-22-2-2-211111111-1-1-1-1-1-1-1-111111100000000000000
χ21222222-12222-1-1-1-2-2-2-22222-1-1111122-1-1-11111-1-1-1-1-12-2-2-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1111100000000000000
χ22222222-12222-1-1-1-2-2-2-22222-1-11111-2-2-1-1-11111-11111-222-2-2-2-222-1-1-1-111111111-1-1-1-111-1-1-1-100000000000000
χ23222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1111122-1-1-11111-1-1-1-1-1-22222-22-2-21111-1-1-1-11111-1-1-1-1-1-1111100000000000000
χ24222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-11111-2-2-1-1-11111-111112-2-2222-2221111-1-1-1-1-1-1-1-1111111-1-1-1-100000000000000
χ252222-2-222-22-2222000022-2-2-2-20000222-2-2000022222-200002-20022-2-2000022-2-20000-2-2000000000000000000
χ262222-2-222-22-2222000022-2-2-2-20000-2-22-2-200002-2-2-2-220000-220022-2-20000-2-222000022000000000000000000
χ272222-2-222-22-22220000-2-222-2-20000222-2-200002222220000-2-200-2-2220000-2-2220000-2-2000000000000000000
χ282222-2-222-22-22220000-2-222-2-20000-2-22-2-200002-2-2-2-2-200002200-2-222000022-2-2000022000000000000000000
χ292222-2-22-22-2222222-2-20000-2-2222200-222-2-2-2-2-2000000000000000000000000000000000002200-220000-2000
χ302222-2-22-22-2222222-2-20000-2-2222200-222-2-2-2-2-200000000000000000000000000000000000-2-2002-200002000
χ312222-2-22-22-22222-2-2220000-2-2-2-2-2-200-2222222-20000000000000000000000000000000000022002-20000-2000
χ322222-2-22-22-22222-2-2220000-2-2-2-2-2-200-2222222-200000000000000000000000000000000000-2-200-2200002000
χ332222-2-2-12-22-2-1-1-1000022-2-211−i3−i3i3i322-111−i3−i3i3i3-1-1-1-1-1-200002-200-1-111−i3−i3i3i3-1-111−i3−i3i3i311−i3−i3i3i300000000000000
χ342222-2-2-12-22-2-1-1-1000022-2-211−i3−i3i3i3-2-2-111−i3−i3i3i3-1111120000-2200-1-111−i3−i3i3i311-1-1i3i3−i3−i3-1-1i3i3−i3−i300000000000000
χ352222-2-2-12-22-2-1-1-1000022-2-211i3i3−i3−i322-111i3i3−i3−i3-1-1-1-1-1-200002-200-1-111i3i3−i3−i3-1-111i3i3−i3−i311i3i3−i3−i300000000000000
χ362222-2-2-12-22-2-1-1-1000022-2-211i3i3−i3−i3-2-2-111i3i3−i3−i3-1111120000-2200-1-111i3i3−i3−i311-1-1−i3−i3i3i3-1-1−i3−i3i3i300000000000000
χ372222-2-2-12-22-2-1-1-10000-2-22211−i3−i3i3i322-111−i3−i3i3i3-1-1-1-1-120000-2-20011-1-1i3i3−i3−i311-1-1i3i3−i3−i311−i3−i3i3i300000000000000
χ382222-2-2-12-22-2-1-1-10000-2-22211−i3−i3i3i3-2-2-111−i3−i3i3i3-11111-20000220011-1-1i3i3−i3−i3-1-111−i3−i3i3i3-1-1i3i3−i3−i300000000000000
χ392222-2-2-12-22-2-1-1-10000-2-22211i3i3−i3−i322-111i3i3−i3−i3-1-1-1-1-120000-2-20011-1-1−i3−i3i3i311-1-1−i3−i3i3i311i3i3−i3−i300000000000000
χ402222-2-2-12-22-2-1-1-10000-2-22211i3i3−i3−i3-2-2-111i3i3−i3−i3-11111-20000220011-1-1−i3−i3i3i3-1-111i3i3−i3−i3-1-1−i3−i3i3i300000000000000
χ4122-2-22-2222-2-22-2-22-22-200002-22-22-20022-22-22-2-200000000000000000000000000000000000002-200002-20000
χ4222-2-22-2222-2-22-2-22-22-200002-22-22-20022-22-22-2-20000000000000000000000000000000000000-220000-220000
χ4322-2-22-2222-2-22-2-2-22-2200002-2-22-220022-2-22-22-200000000000000000000000000000000000002-20000-220000
χ4422-2-22-2222-2-22-2-2-22-2200002-2-22-220022-2-22-22-20000000000000000000000000000000000000-2200002-20000
χ4522-2-22-22-2-2222-2-200002i−2i2i−2i2-2000000-2-2200002000002i−2i00002-22i−2i2i−2i000000002i−2i2i−2i002-22-200000000000000
χ4622-2-22-22-2-2222-2-200002i−2i2i−2i2-2000000-2-220000200000−2i2i0000-222i−2i2i−2i00000000−2i2i−2i2i00-22-2200000000000000
χ4722-2-22-22-2-2222-2-20000−2i2i−2i2i2-2000000-2-2200002000002i−2i0000-22−2i2i−2i2i000000002i−2i2i−2i00-22-2200000000000000
χ4822-2-22-22-2-2222-2-20000−2i2i−2i2i2-2000000-2-220000200000−2i2i00002-2−2i2i−2i2i00000000−2i2i−2i2i002-22-200000000000000
χ4922-2-22-2-1-2-222-11100002i−2i2i−2i-11−i3i3i3−i30011-1i3−i3−i3i3-1−i3−i3i3i302i−2i00002-2−ii−ii3−33−33−33−3−ii−ii−i3i3-11-1100000000000000
χ5022-2-22-2-1-2-222-11100002i−2i2i−2i-11−i3i3i3−i30011-1i3−i3−i3i3-1i3i3−i3−i30−2i2i0000-22−ii−ii3−33−3−33−33i−ii−ii3−i31-11-100000000000000
χ5122-2-22-2-1-2-222-11100002i−2i2i−2i-11i3−i3−i3i30011-1−i3i3i3−i3-1−i3−i3i3i30−2i2i0000-22−ii−ii−33−333−33−3i−ii−i−i3i31-11-100000000000000
χ5222-2-22-2-1-2-222-11100002i−2i2i−2i-11i3−i3−i3i30011-1−i3i3i3−i3-1i3i3−i3−i302i−2i00002-2−ii−ii−33−33−33−33−ii−iii3−i3-11-1100000000000000
χ5322-2-22-2-1-2-222-1110000−2i2i−2i2i-11−i3i3i3−i30011-1i3−i3−i3i3-1−i3−i3i3i30−2i2i00002-2i−ii−i−33−33−33−33i−ii−i−i3i3-11-1100000000000000
χ5422-2-22-2-1-2-222-1110000−2i2i−2i2i-11−i3i3i3−i30011-1i3−i3−i3i3-1i3i3−i3−i302i−2i0000-22i−ii−i−33−333−33−3−ii−iii3−i31-11-100000000000000
χ5522-2-22-2-1-2-222-1110000−2i2i−2i2i-11i3−i3−i3i30011-1−i3i3i3−i3-1−i3−i3i3i302i−2i0000-22i−ii−i3−33−3−33−33−ii−ii−i3i31-11-100000000000000
χ5622-2-22-2-1-2-222-1110000−2i2i−2i2i-11i3−i3−i3i30011-1−i3i3i3−i3-1i3i3−i3−i30−2i2i00002-2i−ii−i3−33−33−33−3i−ii−ii3−i3-11-1100000000000000
χ5722-2-2-222-222-22-2-22-2-222i−2i−2i2i-222-22-200-22-2-22-22200000002i−2i00002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ5822-2-2-222-222-22-2-22-2-22−2i2i2i−2i-222-22-200-22-2-22-2220000000−2i2i0000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ5922-2-2-222-222-22-2-2-222-22i−2i−2i2i-22-22-2200-22-22-22-220000000−2i2i00002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ6022-2-2-222-222-22-2-2-222-2−2i2i2i−2i-22-22-2200-22-22-22-2200000002i−2i0000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ6122-2-2-22-1-222-2-1112-2-222i−2i−2i2i1-1-11-11001-111-11-1-1−i3−i3i3i30002i−2i0000−iii−i−iii−i3−3−333−3−33i3−i3−i3i3i3−i300000000000000
χ6222-2-2-22-1-222-2-1112-2-222i−2i−2i2i1-1-11-11001-111-11-1-1i3i3−i3−i30002i−2i0000−iii−i−iii−i−333−3−333−3−i3i3i3−i3−i3i300000000000000
χ6322-2-2-22-1-222-2-1112-2-22−2i2i2i−2i1-1-11-11001-111-11-1-1−i3−i3i3i3000−2i2i0000i−i−iii−i−ii−333−3−333−3i3−i3−i3i3i3−i300000000000000
χ6422-2-2-22-1-222-2-1112-2-22−2i2i2i−2i1-1-11-11001-111-11-1-1i3i3−i3−i3000−2i2i0000i−i−iii−i−ii3−3−333−3−33−i3i3i3−i3−i3i300000000000000
χ6522-2-2-22-1-222-2-111-222-22i−2i−2i2i1-11-11-1001-11-11-11-1−i3−i3i3i3000−2i2i0000−iii−ii−i−ii3−3−33−333−3i3−i3i3−i3−i3i300000000000000
χ6622-2-2-22-1-222-2-111-222-22i−2i−2i2i1-11-11-1001-11-11-11-1i3i3−i3−i3000−2i2i0000−iii−ii−i−ii−333−33−3−33−i3i3−i3i3i3−i300000000000000
χ6722-2-2-22-1-222-2-111-222-2−2i2i2i−2i1-11-11-1001-11-11-11-1−i3−i3i3i30002i−2i0000i−i−ii−iii−i−333−33−3−33i3−i3i3−i3−i3i300000000000000
χ6822-2-2-22-1-222-2-111-222-2−2i2i2i−2i1-11-11-1001-11-11-11-1i3i3−i3−i30002i−2i0000i−i−ii−iii−i3−3−33−333−3−i3i3−i3i3i3−i300000000000000
χ694444444-4-4-4-44440000000044000000-4-4-40000-40000000000000000000000000000000000000000000000000
χ70444444-2-4-4-4-4-2-2-200000000-2-2−2i3−2i32i32i3002222i32i3−2i3−2i320000000000000000000000000000000000000000000000000
χ71444444-2-4-4-4-4-2-2-200000000-2-22i32i3−2i3−2i300222−2i3−2i32i32i320000000000000000000000000000000000000000000000000
χ724444-4-4-2-44-44-2-2-244-4-4000022-2-2-2-2002-2-2222220000000000000000000000000000000000000000000000000
χ734444-4-4-2-44-44-2-2-2-4-4440000222222002-2-2-2-2-2-220000000000000000000000000000000000000000000000000
χ7444-4-44-4-244-4-4-2224-44-40000-22-22-2200-2-22-22-2220000000000000000000000000000000000000000000000000
χ7544-4-44-4-244-4-4-222-44-440000-222-22-200-2-222-22-220000000000000000000000000000000000000000000000000
χ7644-4-4-4444-4-444-4-400000000-440000004-440000-40000000000000000000000000000000000000000000000000
χ7744-4-4-44-24-4-44-222000000002-2−2i32i32i3−2i300-22-2−2i32i32i3−2i320000000000000000000000000000000000000000000000000
χ7844-4-4-44-24-4-44-222000000002-22i3−2i3−2i32i300-22-22i3−2i3−2i32i320000000000000000000000000000000000000000000000000
χ794-44-40040000-44-400000000000000−2i22i200000000−2i22i2−2i22i20000000000000000000000000000000−2i22i200002-2000000
χ804-44-40040000-44-400000000000000−2i22i200000000−2i22i2−2i22i200000000000000000000000000000002i2−2i20000-22000000
χ814-44-40040000-44-4000000000000002i2−2i2000000002i2−2i22i2−2i20000000000000000000000000000000−2i22i20000-22000000
χ824-44-40040000-44-4000000000000002i2−2i2000000002i2−2i22i2−2i200000000000000000000000000000002i2−2i200002-2000000
χ838-88-800-400004-4400000000000000−4i24i2000000002i2−2i22i2−2i2000000000000000000000000000000000000000000000
χ848-88-800-400004-44000000000000004i2−4i200000000−2i22i2−2i22i2000000000000000000000000000000000000000000000
χ858-8-880080000-8-880000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8800-4000044-400000000000000000000000026−26−2626000000000000000000000000000000000000000000000
χ878-8-8800-4000044-4000000000000000000000000−262626−26000000000000000000000000000000000000000000000

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