Finite Group Databasebeta

← Group #10713337

Character table — Group #10713337

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444466668888888888888888881212121212121616161616161616161624242424242424244848
order12442223444688881212666881212122424242488888888161616162424484848484848484844448888242424242424242444441616161688
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
χ911-1-1-11-1111-11-1-111-1-11-1-11-111-1-1-11111-1-1ii−i−i11-1-11-11111-1-1-1-111-1-11-1i−iii−i−iii−i−iii−i−i11-1-1i−i
χ1011-1-1-11-1111-11-1-111-1-11-1-11-111-1-1-11111-1-1ii−i−i-1-1111-1-1-1-1-1111111-1-11-1−iiii−i−i−i−iiiii−i−i-1-111−ii
χ1111-1-1-11-1111-11-1-111-1-11-1-11-111-1-1-11111-1-1−i−iii11-1-11-11111-1-1-1-111-1-11-1−ii−i−iii−i−iii−i−iii11-1-1−ii
χ1211-1-1-11-1111-11-1-111-1-11-1-11-111-1-1-11111-1-1−i−iii-1-1111-1-1-1-1-1111111-1-11-1i−i−i−iiiii−i−i−i−iii-1-111i−i
χ1311-1-1-11-1111-11-1-111-1-11-1-11-111-1-1-111-1-111ii−i−i11-1-11-11111-1-1-1-1-1-111-11i−iii−i−iii−i−i−i−iii-1-111−ii
χ1411-1-1-11-1111-11-1-111-1-11-1-11-111-1-1-111-1-111ii−i−i-1-1111-1-1-1-1-11111-1-111-11−iiii−i−i−i−iii−i−iii11-1-1i−i
χ1511-1-1-11-1111-11-1-111-1-11-1-11-111-1-1-111-1-111−i−iii11-1-11-11111-1-1-1-1-1-111-11−ii−i−iii−i−iiiii−i−i-1-111i−i
χ1611-1-1-11-1111-11-1-111-1-11-1-11-111-1-1-111-1-111−i−iii-1-1111-1-1-1-1-11111-1-111-11i−i−i−iiiii−i−iii−i−i11-1-1−ii
χ17222222222222-2-2-2-222222-2-2222-2-2-2-2222200000000-2-200000000-2-2-2-22200000000000000000000
χ18222222222222-2-2-2-222222-2-2222-2-2-2-2-2-2-2-200000000-2-2000000002222-2-200000000000000000000
χ192222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-1000022222222-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-1-1-10000000000
χ202222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-100002222-2-2-2-2-1-111111111000000-2-2-1-1-1-111110000000000
χ212222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-10000-2-2-2-22222-1-1-1-1-1-1-1-1-1-1000000-2-2111111110000000000
χ222222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-2-1-111111111000000221111-1-1-1-10000000000
χ2322222-2-222-2-22222222-22-2-2-2-22-22222000000000000-2-20000000000000000000000002i−2i2i−2i000000
χ2422222-2-222-2-22222222-22-2-2-2-22-22222000000000000-2-2000000000000000000000000−2i2i−2i2i000000
χ2522222-2-222-2-22-2-2-2-222-22-222-22-2-2-2-2-200002-22-200002200000000000000002-22-200000000000000
χ2622222-2-222-2-22-2-2-2-222-22-222-22-2-2-2-2-20000-22-220000220000000000000000-22-2200000000000000
χ2722222-2-2-12-2-2-1-2-2-2-2-1-11-11221-11111100002-22-20000-1-133−3−333−3−300000000-11-113−33−30000000000
χ2822222-2-2-12-2-2-1-2-2-2-2-1-11-11221-11111100002-22-20000-1-1−3−333−3−33300000000-11-11−33−330000000000
χ2922222-2-2-12-2-2-1-2-2-2-2-1-11-11221-1111110000-22-220000-1-133−3−333−3−3000000001-11-1−33−330000000000
χ3022222-2-2-12-2-2-1-2-2-2-2-1-11-11221-1111110000-22-220000-1-1−3−333−3−333000000001-11-13−33−30000000000
χ312222-2-222-22-22000022-2-22002-2-2000022220000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i20000-2-200000000000000−i2i2−i2i200
χ322222-2-222-22-22000022-2-22002-2-2000022220000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i20000-2-200000000000000i2−i2i2−i200
χ332222-2-222-22-22000022-2-22002-2-20000-2-2-2-20000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i200002200000000000000i2−i2i2−i200
χ342222-2-222-22-22000022-2-22002-2-20000-2-2-2-20000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i200002200000000000000−i2i2−i2i200
χ3522-2-22-2-22-22220000-2-2-22-2002-22000022-2-20000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i20000-2200000000000000−i2i2i2−i200
χ3622-2-22-2-22-22220000-2-2-22-2002-22000022-2-20000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i20000-2200000000000000i2−i2−i2i200
χ3722-2-22-2-22-22220000-2-2-22-2002-220000-2-2220000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i200002-200000000000000i2−i2−i2i200
χ3822-2-22-2-22-22220000-2-2-22-2002-220000-2-2220000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i200002-200000000000000−i2i2i2−i200
χ3922-2-2-22-2222-2222-2-2-2-22-2-2-2222-222-2-222-2-200000000-2200000000-2-2222-200000000000000000000
χ4022-2-2-22-2222-2222-2-2-2-22-2-2-2222-222-2-2-2-22200000000-220000000022-2-2-2200000000000000000000
χ4122-2-2-22-2-122-2-1-2-22211-1112-2-1-1111-1-100002i2i−2i−2i22-2-2-11-1-1-1-111110000002i−2i−i−iii−i−iii0000000000
χ4222-2-2-22-2-122-2-1-2-22211-1112-2-1-1111-1-100002i2i−2i−2i-2-222-111111-1-1-1-1000000−2i2i−i−iiiii−i−i0000000000
χ4322-2-2-22-2-122-2-1-2-22211-1112-2-1-1111-1-10000−2i−2i2i2i22-2-2-11-1-1-1-11111000000−2i2iii−i−iii−i−i0000000000
χ4422-2-2-22-2-122-2-1-2-22211-1112-2-1-1111-1-10000−2i−2i2i2i-2-222-111111-1-1-1-10000002i−2iii−i−i−i−iii0000000000
χ4522-2-2-2-2222-22222-2-2-2-2-2-222-2-22222-2-200002i−2i−2i2i00002-200000000000000002i−2i−2i2i00000000000000
χ4622-2-2-2-2222-22222-2-2-2-2-2-222-2-22222-2-20000−2i2i2i−2i00002-20000000000000000−2i2i2i−2i00000000000000
χ4722-2-2-2-2222-222-2-222-2-2-2-22-22-222-2-222000000000000-220000000000000000000000002-2-22000000
χ4822-2-2-2-2222-222-2-222-2-2-2-22-22-222-2-222000000000000-22000000000000000000000000-222-2000000
χ4922-2-2-2-22-12-22-122-2-21111-12-21-1-1-1-11100002i−2i−2i2i0000-1133−3−3−3−33300000000−iii−ii3−i3−i3i30000000000
χ5022-2-2-2-22-12-22-122-2-21111-12-21-1-1-1-11100002i−2i−2i2i0000-11−3−33333−3−300000000−iii−i−i3i3i3−i30000000000
χ5122-2-2-2-22-12-22-122-2-21111-12-21-1-1-1-1110000−2i2i2i−2i0000-1133−3−3−3−33300000000i−i−ii−i3i3i3−i30000000000
χ5222-2-2-2-22-12-22-122-2-21111-12-21-1-1-1-1110000−2i2i2i−2i0000-11−3−33333−3−300000000i−i−iii3−i3−i3i30000000000
χ534444444-2444-2-4-4-4-4-2-2-2-2-2-4-4-2-2-22222000000000000220000000000000000000000000000000000
χ5444444-4-4-24-4-4-24444-2-22-22-4-42-22-2-2-2-2000000000000220000000000000000000000000000000000
χ554444-44-44-4-4440000444-4-400-4-440000000000000000000000000000000000000000000000000000
χ564444-44-4-2-4-44-20000-2-2-2220022-2000000000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ574444-44-4-2-4-44-20000-2-2-2220022-2000000000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ584444-4-44-2-44-4-20000-2-222-200-222000000000000−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ594444-4-44-2-44-4-20000-2-222-200-2220000000000002i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ6044-4-44444-4-4-440000-4-444400-4-4-40000000000000000000000000000000000000000000000000000
χ6144-4-4444-2-4-4-4-2000022-2-2-200222000000000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ6244-4-4444-2-4-4-4-2000022-2-2-200222000000000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ6344-4-44-4-4-2-444-20000222-2200-22-2000000000000−2i22i22i2−2i200i2−i2i2−i2−i2i2−i2i200000000000000000000000000
χ6444-4-44-4-4-2-444-20000222-2200-22-20000000000002i2−2i2−2i22i200−i2i2−i2i2i2−i2i2−i200000000000000000000000000
χ6544-4-4-44-4-244-4-244-4-422-222-44-2-22-2-2220000000000002-20000000000000000000000000000000000
χ6644-4-4-4-44-24-44-2-4-4442222-2-442-2-222-2-20000000000002-20000000000000000000000000000000000
χ674-44i−4i0004000-422−22−2i22i24i−4i0000000022−22−2i22i222−22−2i22i20000000000000000002i−2i2-20000000000000000000000
χ684-44i−4i0004000-422−22−2i22i24i−4i0000000022−22−2i22i2−22222i2−2i2000000000000000000−2i2i-220000000000000000000000
χ694-44i−4i0004000-4−22222i2−2i24i−4i00000000−22222i2−2i222−22−2i22i2000000000000000000−2i2i-220000000000000000000000
χ704-44i−4i0004000-4−22222i2−2i24i−4i00000000−22222i2−2i2−22222i2−2i20000000000000000002i−2i2-20000000000000000000000
χ714-4−4i4i0004000-422−222i2−2i2−4i4i0000000022−222i2−2i222−222i2−2i2000000000000000000−2i2i2-20000000000000000000000
χ724-4−4i4i0004000-422−222i2−2i2−4i4i0000000022−222i2−2i2−2222−2i22i20000000000000000002i−2i-220000000000000000000000
χ734-4−4i4i0004000-4−2222−2i22i2−4i4i00000000−2222−2i22i222−222i2−2i20000000000000000002i−2i-220000000000000000000000
χ744-4−4i4i0004000-4−2222−2i22i2−4i4i00000000−2222−2i22i2−2222−2i22i2000000000000000000−2i2i2-20000000000000000000000
χ758-88i−8i000-4000442−42−4i24i2−4i4i00000000−22222i2−2i2000000000000000000000000000000000000000000000000
χ768-88i−8i000-40004−42424i2−4i2−4i4i0000000022−22−2i22i2000000000000000000000000000000000000000000000000
χ778-8−8i8i000-4000442−424i2−4i24i−4i00000000−2222−2i22i2000000000000000000000000000000000000000000000000
χ788-8−8i8i000-40004−4242−4i24i24i−4i0000000022−222i2−2i2000000000000000000000000000000000000000000000000

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