Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×#10621462 |
| derived | SL(2,𝔽7) ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, socle, hypercenter | C22 | SO(3,𝔽7) |
| commutator, cosocle, hypocenter | SL(2,𝔽7) | C22 |
| Frattini | C2 | C2×SO(3,𝔽7) |
| LCS | G ▷ SL(2,𝔽7) | |
| UCS | C1 ◁ C22 | |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32 |
32 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#10621462, D3×#10621462, C4×#10621462 |
| maximal normal subgroup of | C2×C3×#10621462, C4×#10621462 |
| maximal quotient of | C2×C3×#10621462, D3×#10621462, C4×#10621462 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11296);