Finite Group DatabasebetaFinite Group Databasebeta| order | 16317 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C37 · Schur multiplier (H2) = C3 |
| direct product | ΓL(1,𝔽8)2×C37 |
| unambiguous semidirect product | (C7×ΓL(1,𝔽8))⋊(C3×C37) |
| unambiguous semidirect product | #3861⋊(C3×C37) |
| unambiguous semidirect product | #3862⋊(C3×C37) |
| Fitting, socle, Hall | C72×C37 ⋊ C32 |
| derived, Sylow | C72 ⋊ C32×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | ΓL(1,𝔽8)2 |
| commutator, cosocle, hypocenter | C72 | C32×C37 |
| Frattini | C1 | G |
| Fitting, socle | C72×C37 | C32 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C37 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 777 |
925 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#64418⋊C3, #45657389, ΓL(1,𝔽8)2×D37, … |
| maximal normal subgroup of | C37×#64418⋊C3, #45657389, ΓL(1,𝔽8)2×D37, … |
| maximal quotient of | C2×ΓL(1,𝔽8)2×C37 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16317, 35);