Finite Group Databasebeta

← Group #10713332

Character table — Group #10713332

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444466668888888888888888881212121212121616161616161616161624242424242424244848
order1222223444466688886688121212122424242488884444161616162424484848484848484844448844121212121212121288881616161644
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ5111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
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
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1
χ911-1-11-11-111-11-1-1-1-1111-11-11-1-11-1-11111-1-1ii−i−i11-1-11-11111-1-1-1-111-1-11-1i−iii−i−iii−i−iii−i−i11-1-1i−i
χ1011-1-11-11-111-11-1-1-1-1111-11-11-1-11-1-11111-1-1ii−i−i-1-1111-1-1-1-1-1111111-1-11-1−iiii−i−i−i−iiiii−i−i-1-111−ii
χ1111-1-11-11-111-11-1-1-1-1111-11-11-1-11-1-11111-1-1−i−iii11-1-11-11111-1-1-1-111-1-11-1−ii−i−iii−i−iii−i−iii11-1-1−ii
χ1211-1-11-11-111-11-1-1-1-1111-11-11-1-11-1-11111-1-1−i−iii-1-1111-1-1-1-1-1111111-1-11-1i−i−i−iiiii−i−i−i−iii-1-111i−i
χ1311-1-11-11-111-11-1-1-1-1111-11-11-1-11-1-111-1-111ii−i−i11-1-11-11111-1-1-1-1-1-111-11i−iii−i−iii−i−i−i−iii-1-111−ii
χ1411-1-11-11-111-11-1-1-1-1111-11-11-1-11-1-111-1-111ii−i−i-1-1111-1-1-1-1-11111-1-111-11−iiii−i−i−i−iii−i−iii11-1-1i−i
χ1511-1-11-11-111-11-1-1-1-1111-11-11-1-11-1-111-1-111−i−iii11-1-11-11111-1-1-1-1-1-111-11−ii−i−iii−i−iiiii−i−i-1-111i−i
χ1611-1-11-11-111-11-1-1-1-1111-11-11-1-11-1-111-1-111−i−iii-1-1111-1-1-1-1-11111-1-111-11i−i−i−iiiii−i−iii−i−i11-1-1−ii
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
χ20222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-100002222-2-2-2-2-1-111111111000000-2-2-1-1-1-111110000000000
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
χ22222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-2-1-111111111000000221111-1-1-1-10000000000
χ232222-2-2222-2-22222222-2-2-2-2-22-222222000000000000-2-20000000000000000000000002i−2i2i−2i000000
χ242222-2-2222-2-22222222-2-2-2-2-22-222222000000000000-2-2000000000000000000000000−2i2i−2i2i000000
χ252222-2-2222-2-2222-2-2-2-2-2-222-22-22-2-2-2-200002-22-200002200000000000000002-22-200000000000000
χ262222-2-2222-2-2222-2-2-2-2-2-222-22-22-2-2-2-20000-22-220000220000000000000000-22-2200000000000000
χ272222-2-22-2-2222220000-2-2002-22-2000022220000−i2i2−i2i200−i2−i2i2i2−i2−i2i2i20000-2-200000000000000−i2i2−i2i200
χ282222-2-22-2-2222220000-2-2002-22-2000022220000i2−i2i2−i200i2i2−i2−i2i2i2−i2−i20000-2-200000000000000i2−i2i2−i200
χ292222-2-22-2-2222220000-2-2002-22-20000-2-2-2-20000−i2i2−i2i200−i2−i2i2i2−i2−i2i2i200002200000000000000i2−i2i2−i200
χ302222-2-22-2-2222220000-2-2002-22-20000-2-2-2-20000i2−i2i2−i200i2i2−i2−i2i2i2−i2−i200002200000000000000−i2i2−i2i200
χ312222-2-2-122-2-2-1-1-1-2-2-2-211221-11-1111100002-22-20000-1-13−33−33−33−300000000-11-113−33−30000000000
χ322222-2-2-122-2-2-1-1-1-2-2-2-211221-11-1111100002-22-20000-1-1−33−33−33−3300000000-11-11−33−330000000000
χ332222-2-2-122-2-2-1-1-1-2-2-2-211221-11-111110000-22-220000-1-13−33−33−33−3000000001-11-1−33−330000000000
χ342222-2-2-122-2-2-1-1-1-2-2-2-211221-11-111110000-22-220000-1-1−33−33−33−33000000001-11-13−33−30000000000
χ3522-2-22-22-222-22-2-222-2-22-2-222-2-2222-2-222-2-200000000-2200000000-2-2222-200000000000000000000
χ3622-2-22-22-222-22-2-222-2-22-2-222-2-2222-2-2-2-22200000000-220000000022-2-2-2200000000000000000000
χ3722-2-22-2-1-222-2-111-2-222-112-2-111-111-1-100002i2i−2i−2i22-2-2-11-1-1-1-111110000002i−2i−i−iii−i−iii0000000000
χ3822-2-22-2-1-222-2-111-2-222-112-2-111-111-1-100002i2i−2i−2i-2-222-111111-1-1-1-1000000−2i2i−i−iiiii−i−i0000000000
χ3922-2-22-2-1-222-2-111-2-222-112-2-111-111-1-10000−2i−2i2i2i22-2-2-11-1-1-1-11111000000−2i2iii−i−iii−i−i0000000000
χ4022-2-22-2-1-222-2-111-2-222-112-2-111-111-1-10000−2i−2i2i2i-2-222-111111-1-1-1-10000002i−2iii−i−i−i−iii0000000000
χ4122-2-2-2222-22-22-2-20000-220022-2-2000022-2-20000−i2i2i2−i200−i2−i2i2i2i2i2−i2−i20000-2200000000000000−i2i2i2−i200
χ4222-2-2-2222-22-22-2-20000-220022-2-2000022-2-20000i2−i2−i2i200i2i2−i2−i2−i2−i2i2i20000-2200000000000000i2−i2−i2i200
χ4322-2-2-2222-22-22-2-20000-220022-2-20000-2-2220000−i2i2i2−i200−i2−i2i2i2i2i2−i2−i200002-200000000000000i2−i2−i2i200
χ4422-2-2-2222-22-22-2-20000-220022-2-20000-2-2220000i2−i2−i2i200i2i2−i2−i2−i2−i2i2i200002-200000000000000−i2i2i2−i200
χ4522-2-2-222-22-222-2-222-2-2-222-2-2-22222-2-200002i−2i−2i2i00002-200000000000000002i−2i−2i2i00000000000000
χ4622-2-2-222-22-222-2-222-2-2-222-2-2-22222-2-20000−2i2i2i−2i00002-20000000000000000−2i2i2i−2i00000000000000
χ4722-2-2-222-22-222-2-2-2-222-22-22-2-222-2-222000000000000-220000000000000000000000002-2-22000000
χ4822-2-2-222-22-222-2-2-2-222-22-22-2-222-2-222000000000000-22000000000000000000000000-222-2000000
χ4922-2-2-22-1-22-22-11122-2-21-12-211-1-1-1-11100002i−2i−2i2i0000-113−33−3−33−3300000000−iii−ii3−i3−i3i30000000000
χ5022-2-2-22-1-22-22-11122-2-21-12-211-1-1-1-11100002i−2i−2i2i0000-11−33−333−33−300000000−iii−i−i3i3i3−i30000000000
χ5122-2-2-22-1-22-22-11122-2-21-12-211-1-1-1-1110000−2i2i2i−2i0000-113−33−3−33−3300000000i−i−ii−i3i3i3−i30000000000
χ5222-2-2-22-1-22-22-11122-2-21-12-211-1-1-1-1110000−2i2i2i−2i0000-11−33−333−33−300000000i−i−iii3−i3−i3i30000000000
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
χ55444444-2-4-4-4-4-2-2-20000-2-2002222000000000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ56444444-2-4-4-4-4-2-2-20000-2-2002222000000000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ574444-4-4-244-4-4-2-2-2444422-4-42-22-2-2-2-2-2000000000000220000000000000000000000000000000000
χ584444-4-4-2-4-444-2-2-200002200-22-22000000000000−2i22i2−2i22i200i2i2−i2−i2i2i2−i2−i200000000000000000000000000
χ594444-4-4-2-4-444-2-2-200002200-22-220000000000002i2−2i22i2−2i200−i2−i2i2i2−i2−i2i2i200000000000000000000000000
χ6044-4-44-444-4-444-4-400004-400-444-40000000000000000000000000000000000000000000000000000
χ6144-4-44-4-24-4-44-2220000-22002-2-22000000000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ6244-4-44-4-24-4-44-2220000-22002-2-22000000000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ6344-4-44-4-2-444-4-22244-4-4-22-44-222-2-2-2220000000000002-20000000000000000000000000000000000
χ6444-4-4-44-24-44-4-22200002-200-2-222000000000000−2i22i22i2−2i200i2i2−i2−i2−i2−i2i2i200000000000000000000000000
χ6544-4-4-44-24-44-4-22200002-200-2-2220000000000002i2−2i2−2i22i200−i2−i2i2i2i2i2−i2−i200000000000000000000000000
χ6644-4-4-44-2-44-44-222-4-4442-2-4422-2-222-2-20000000000002-20000000000000000000000000000000000
χ674-44-40040000-44-4−2i22i2−2i22i200000000−2i22i2−2i22i222−2222−220000000000000000002i−2i2i−2i0000000000000000000000
χ684-44-40040000-44-4−2i22i2−2i22i200000000−2i22i2−2i22i2−2222−2222000000000000000000−2i2i−2i2i0000000000000000000000
χ694-44-40040000-44-42i2−2i22i2−2i2000000002i2−2i22i2−2i222−2222−22000000000000000000−2i2i−2i2i0000000000000000000000
χ704-44-40040000-44-42i2−2i22i2−2i2000000002i2−2i22i2−2i2−2222−22220000000000000000002i−2i2i−2i0000000000000000000000
χ714-4-440040000-4-44−2i22i22i2−2i200000000−2i22i22i2−2i222−22−2222000000000000000000−2i2i2i−2i0000000000000000000000
χ724-4-440040000-4-44−2i22i22i2−2i200000000−2i22i22i2−2i2−222222−220000000000000000002i−2i−2i2i0000000000000000000000
χ734-4-440040000-4-442i2−2i2−2i22i2000000002i2−2i2−2i22i222−22−22220000000000000000002i−2i−2i2i0000000000000000000000
χ744-4-440040000-4-442i2−2i2−2i22i2000000002i2−2i2−2i22i2−222222−22000000000000000000−2i2i2i−2i0000000000000000000000
χ758-88-800-400004-44−4i24i2−4i24i2000000002i2−2i22i2−2i2000000000000000000000000000000000000000000000000
χ768-88-800-400004-444i2−4i24i2−4i200000000−2i22i2−2i22i2000000000000000000000000000000000000000000000000
χ778-8-8800-4000044-4−4i24i24i2−4i2000000002i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ788-8-8800-4000044-44i2−4i2−4i24i200000000−2i22i22i2−2i2000000000000000000000000000000000000000000000000

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