Finite Group Databasebeta

← Group #10713689

Character table — Group #10713689

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444466668888888888888888881212121212121616161616161616161624242424242424244848
order1222223444466688886688121212122424242488888888161616162424484848484848484844448844121212122424242444441616161622
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ5111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1
χ911-1-1-111-11-11-1-1111-1-11-11-11-11-111-1-111-1-1ii−i−iii−i−i1-1iiii−i−i−i−i11-1-11-11-111-1-1ii−i−iii−i−iii−i−i1-1
χ1011-1-1-111-11-11-1-1111-1-11-11-11-11-111-1-111-1-1ii−i−i−i−iii1-1−i−i−i−iiiii11-1-11-1-11-1-111ii−i−iii−i−i−i−iii-11
χ1111-1-1-111-11-11-1-1111-1-11-11-11-11-111-1-111-1-1−i−iiiii−i−i1-1iiii−i−i−i−i11-1-11-1-11-1-111−i−iii−i−iiiii−i−i-11
χ1211-1-1-111-11-11-1-1111-1-11-11-11-11-111-1-111-1-1−i−iii−i−iii1-1−i−i−i−iiiii11-1-11-11-111-1-1−i−iii−i−iii−i−iii1-1
χ1311-1-1-111-11-11-1-1111-1-11-11-11-11-111-1-1-1-111ii−i−iii−i−i1-1iiii−i−i−i−i-1-111-111-111-1-1ii−i−i−i−iii−i−iii-11
χ1411-1-1-111-11-11-1-1111-1-11-11-11-11-111-1-1-1-111ii−i−i−i−iii1-1−i−i−i−iiiii-1-111-11-11-1-111ii−i−i−i−iiiii−i−i1-1
χ1511-1-1-111-11-11-1-1111-1-11-11-11-11-111-1-1-1-111−i−iiiii−i−i1-1iiii−i−i−i−i-1-111-11-11-1-111−i−iiiii−i−i−i−iii1-1
χ1611-1-1-111-11-11-1-1111-1-11-11-11-11-111-1-1-1-111−i−iii−i−iii1-1−i−i−i−iiiii-1-111-111-111-1-1−i−iiiii−i−iii−i−i-11
χ1722222222222222-2-2-2-222-2-22222-2-2-2-2222200000000-2-200000000-2-2-2-22200000000000000000000
χ1822222222222222-2-2-2-222-2-22222-2-2-2-2-2-2-2-200000000-2-2000000002222-2-200000000000000000000
χ19222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-1000022222222-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-1-1-10000000000
χ20222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-100002222-2-2-2-2-1-111111111000000-2-21111-1-1-1-10000000000
χ21222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-10000-2-2-2-22222-1-1-1-1-1-1-1-1-1-1000000-2-2111111110000000000
χ22222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-2-1-11111111100000022-1-1-1-111110000000000
χ232222-2-2222-2-22222222-2-2-2-2-222-22222000000000000-2-20000000000000000000000002-22-2000000
χ242222-2-2222-2-22222222-2-2-2-2-222-22222000000000000-2-2000000000000000000000000-22-22000000
χ252222-2-2222-2-2222-2-2-2-2-2-222-222-2-2-2-2-200002i−2i2i−2i000022000000000000000000002i−2i2i−2i0000000000
χ262222-2-2222-2-2222-2-2-2-2-2-222-222-2-2-2-2-20000−2i2i−2i2i00002200000000000000000000−2i2i−2i2i0000000000
χ272222-2-22-2-2222220000-2-2002-2-220000222200002−22−20022−2−222−2−20000-2-2000000000000002−22−200
χ282222-2-22-2-2222220000-2-2002-2-22000022220000−22−2200−2−222−2−2220000-2-200000000000000−22−2200
χ292222-2-22-2-2222220000-2-2002-2-220000-2-2-2-200002−22−20022−2−222−2−200002200000000000000−22−2200
χ302222-2-22-2-2222220000-2-2002-2-220000-2-2-2-20000−22−2200−2−222−2−222000022000000000000002−22−200
χ312222-2-2-122-2-2-1-1-1-2-2-2-211221-1-11111100002i−2i2i−2i0000-1-13−33−33−33−300000000−i3i3−i3i3−ii−ii0000000000
χ322222-2-2-122-2-2-1-1-1-2-2-2-211221-1-11111100002i−2i2i−2i0000-1-1−33−33−33−3300000000i3−i3i3−i3−ii−ii0000000000
χ332222-2-2-122-2-2-1-1-1-2-2-2-211221-1-1111110000−2i2i−2i2i0000-1-13−33−33−33−300000000i3−i3i3−i3i−ii−i0000000000
χ342222-2-2-122-2-2-1-1-1-2-2-2-211221-1-1111110000−2i2i−2i2i0000-1-1−33−33−33−3300000000−i3i3−i3i3i−ii−i0000000000
χ3522-2-22-222-2-22-2-220000-220022-2-2000022-2-20000−i2i2i2−i200−i2−i2i2i2i2i2−i2−i20000-2200000000000000−i2i2i2−i200
χ3622-2-22-222-2-22-2-220000-220022-2-2000022-2-20000i2−i2−i2i200i2i2−i2−i2−i2−i2i2i20000-2200000000000000i2−i2−i2i200
χ3722-2-22-222-2-22-2-220000-220022-2-20000-2-2220000−i2i2i2−i200−i2−i2i2i2i2i2−i2−i200002-200000000000000i2−i2−i2i200
χ3822-2-22-222-2-22-2-220000-220022-2-20000-2-2220000i2−i2−i2i200i2i2−i2−i2−i2−i2i2i200002-200000000000000−i2i2i2−i200
χ3922-2-22-22-222-2-2-2222-2-2-22-22-2-22222-2-2000000000000-220000000000000000000000002i−2i−2i2i000000
χ4022-2-22-22-222-2-2-2222-2-2-22-22-2-22222-2-2000000000000-22000000000000000000000000−2i2i2i−2i000000
χ4122-2-22-22-222-2-2-22-2-222-222-2-2-222-2-22200002-2-2200002-2000000000000000000002-2-220000000000
χ4222-2-22-22-222-2-2-22-2-222-222-2-2-222-2-2220000-222-200002-200000000000000000000-222-20000000000
χ4322-2-22-2-1-222-211-1-2-2221-12-211-1-111-1-100002-2-220000-11−i3i3−i3i3i3−i3i3−i300000000−i3i3i3−i3-111-10000000000
χ4422-2-22-2-1-222-211-1-2-2221-12-211-1-111-1-100002-2-220000-11i3−i3i3−i3−i3i3−i3i300000000i3−i3−i3i3-111-10000000000
χ4522-2-22-2-1-222-211-1-2-2221-12-211-1-111-1-10000-222-20000-11−i3i3−i3i3i3−i3i3−i300000000i3−i3−i3i31-1-110000000000
χ4622-2-22-2-1-222-211-1-2-2221-12-211-1-111-1-10000-222-20000-11i3−i3i3−i3−i3i3−i3i300000000−i3i3i3−i31-1-110000000000
χ4722-2-2-222-22-22-2-22-2-2222-2-222-22-2-2-22222-2-200000000-2200000000-2-2222-200000000000000000000
χ4822-2-2-222-22-22-2-22-2-2222-2-222-22-2-2-222-2-22200000000-220000000022-2-2-2200000000000000000000
χ4922-2-2-22-1-22-2211-122-2-2-112-2-11-11-1-11100002i2i−2i−2i2i2i−2i−2i-11−i−i−i−iiiii0000002-2-1-111−i−iii0000000000
χ5022-2-2-22-1-22-2211-122-2-2-112-2-11-11-1-11100002i2i−2i−2i−2i−2i2i2i-11iiii−i−i−i−i000000-2211-1-1−i−iii0000000000
χ5122-2-2-22-1-22-2211-122-2-2-112-2-11-11-1-1110000−2i−2i2i2i2i2i−2i−2i-11−i−i−i−iiiii000000-2211-1-1ii−i−i0000000000
χ5222-2-2-22-1-22-2211-122-2-2-112-2-11-11-1-1110000−2i−2i2i2i−2i−2i2i2i-11iiii−i−i−i−i0000002-2-1-111ii−i−i0000000000
χ534444444-4-4-4-444400004400-4-4-4-40000000000000000000000000000000000000000000000000000
χ54444444-24444-2-2-2-4-4-4-4-2-2-4-4-2-2-2-22222000000000000220000000000000000000000000000000000
χ55444444-2-4-4-4-4-2-2-20000-2-20022220000000000000000006−6−666−6−6600000000000000000000000000
χ56444444-2-4-4-4-4-2-2-20000-2-2002222000000000000000000−666−6−666−600000000000000000000000000
χ574444-4-4-244-4-4-2-2-2444422-4-42-2-22-2-2-2-2000000000000220000000000000000000000000000000000
χ584444-4-4-2-4-444-2-2-200002200-222-200000000000022−2222−2200−2−222−2−22200000000000000000000000000
χ594444-4-4-2-4-444-2-2-200002200-222-2000000000000−2222−22220022−2−222−2−200000000000000000000000000
χ6044-4-44-4-24-4-4422-200002-200-2-222000000000000−2i22i22i2−2i200i2i2−i2−i2−i2−i2i2i200000000000000000000000000
χ6144-4-44-4-24-4-4422-200002-200-2-2220000000000002i2−2i2−2i22i200−i2−i2i2i2i2i2−i2−i200000000000000000000000000
χ6244-4-44-4-2-444-422-244-4-42-2-4422-2-2-2-2220000000000002-20000000000000000000000000000000000
χ6344-4-4-4444-44-4-4-4400004-400-44-440000000000000000000000000000000000000000000000000000
χ6444-4-4-44-24-44-422-20000-22002-22-2000000000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ6544-4-4-44-24-44-422-20000-22002-22-2000000000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ6644-4-4-44-2-44-4422-2-4-444-22-44-22-2222-2-20000000000002-20000000000000000000000000000000000
χ674-44-400400004-4-422−2222−220000000022−2222−22−2i22i2−2i22i20000000000000000002i−2i2i−2i0000000000000000000000
χ684-44-400400004-4-422−2222−220000000022−2222−222i2−2i22i2−2i2000000000000000000−2i2i−2i2i0000000000000000000000
χ694-44-400400004-4-4−2222−222200000000−2222−2222−2i22i2−2i22i2000000000000000000−2i2i−2i2i0000000000000000000000
χ704-44-400400004-4-4−2222−222200000000−2222−22222i2−2i22i2−2i20000000000000000002i−2i2i−2i0000000000000000000000
χ714-4-440040000-44-422−22−22220000000022−22−2222−2i22i22i2−2i20000000000000000002i−2i−2i2i0000000000000000000000
χ724-4-440040000-44-422−22−22220000000022−22−22222i2−2i2−2i22i2000000000000000000−2i2i2i−2i0000000000000000000000
χ734-4-440040000-44-4−222222−2200000000−222222−22−2i22i22i2−2i2000000000000000000−2i2i2i−2i0000000000000000000000
χ744-4-440040000-44-4−222222−2200000000−222222−222i2−2i2−2i22i20000000000000000002i−2i−2i2i0000000000000000000000
χ758-88-800-40000-44442−4242−4200000000−2222−2222000000000000000000000000000000000000000000000000
χ768-88-800-40000-444−4242−42420000000022−2222−22000000000000000000000000000000000000000000000000
χ778-8-8800-400004-4442−42−424200000000−222222−22000000000000000000000000000000000000000000000000
χ788-8-8800-400004-44−424242−420000000022−22−2222000000000000000000000000000000000000000000000000

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