Finite Group DatabasebetaFinite Group Databasebeta| order | 3948 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic141 |
| unambiguous semidirect product | C3⋊(C7×Dic47) |
| unambiguous semidirect product | C47⋊(C7×Dic3) |
| derived, Hall | C3×C47 ⋊ C4×C7 |
| Hall | C3×C7×C47 ⋊ C4 |
| Hall | C7×C47 ⋊ Dic3 |
| Sylow | C47 ⋊ C7×Dic3 |
| Hall | C3×C7 ⋊ Dic47 |
| Sylow | C3 ⋊ C7×Dic47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D141 |
| commutator, hypocenter | C3×C47 | C4×C7 |
| Frattini | C2 | C7×D141 |
| Fitting, socle, prime radical | C2×C3×C7×C47 | C2 |
| cosocle | C2×C3×C47 | C2×C7 |
| LCS | G ▷ C3×C47 | |
| UCS | C1 ◁ C2×C7 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 3948 |
1008 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×Dic423, ΓL(1,𝔽8)×Dic141, C3×C7×Dic141, … |
| maximal normal subgroup of | ΓL(1,𝔽8)×Dic141, C3×C7×Dic141, C5×C7×Dic141, … |
| maximal quotient of | C7×Dic423, C3×C7×Dic141, C7×C3⋊Dic141, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3948, 10);