Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | GL(3,𝔽2)⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×SO(3,𝔽7) |
| commutator, socle, prime radical, cosocle | C2×GL(3,𝔽2) | C22 |
| Fitting, hypercenter | C4 | SO(3,𝔽7) |
| hypocenter | GL(3,𝔽2) | Q8 |
| LCS | G ▷ C2×GL(3,𝔽2) ▷ GL(3,𝔽2) | |
| UCS | C1 ◁ C2 ◁ C4 | |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 56 |
Permutation generators:
(1,5,2,6)(3,7,4,8)(9,12,10,14,15,16,11,13);(1,3,2,4)(5,8,6,7)(9,14,15,13,16,10)24 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11290);