Finite Group DatabasebetaFinite Group Databasebeta| order | 4956 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic177 |
| unambiguous semidirect product | C3⋊(C7×Dic59) |
| unambiguous semidirect product | C59⋊(C7×Dic3) |
| derived, Hall | C3×C59 ⋊ C4×C7 |
| Hall | C3×C7×C59 ⋊ C4 |
| Hall | C7×C59 ⋊ Dic3 |
| Sylow | C59 ⋊ C7×Dic3 |
| Hall | C3×C7 ⋊ Dic59 |
| Sylow | C3 ⋊ C7×Dic59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D177 |
| commutator, hypocenter | C3×C59 | C4×C7 |
| Frattini | C2 | C7×D177 |
| Fitting, socle | C2×C3×C7×C59 | C2 |
| LCS | G ▷ C3×C59 | |
| UCS | C1 ◁ C2×C7 | |
24 conjugacy classes of subgroups.
1260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×Dic531, ΓL(1,𝔽8)×Dic177, C3×C7×Dic177, … |
| maximal normal subgroup of | ΓL(1,𝔽8)×Dic177, C3×C7×Dic177, C5×C7×Dic177, … |
| maximal quotient of | C7×Dic531, C3×C7×Dic177, C7×C3⋊Dic177, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4956, 7);