Finite Group DatabasebetaFinite Group Databasebeta| order | 3708 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D9×D103 |
| unambiguous semidirect product | (D9×C103)⋊C2 |
| unambiguous semidirect product | (C9×D103)⋊C2 |
| unambiguous semidirect product | D927⋊C2 |
| Fitting, derived, Hall | C9×C103 ⋊ C22 |
| Sylow | C103 ⋊ C2×D9 |
| Sylow | C9 ⋊ C2×D103 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C103 | C22 |
| Frattini | C3 | D3×D103 |
| socle | C3×C103 | C2×D3 |
| LCS | G ▷ C9×C103 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 112 |
| transitive degree | μt(G) = 927 |
318 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D9×D103, D45×D103, D9×D515, … |
| maximal normal subgroup of | C5×D9×D103, C7×D9×D103 |
| maximal quotient of | C5×D9×D103, D45×D103, D9×D515, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3708, 9);