Finite Group DatabasebetaFinite Group Databasebeta| order | 4953 |
| isoclinism | isoclinic class of C127⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C127⋊C3 |
| unambiguous semidirect product | C127⋊(C3×C13) |
| Fitting, socle, Hall | C13×C127 ⋊ C3 |
| derived, Sylow | C127 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C127⋊C3 |
| commutator, hypocenter | C127 | C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C127 | C3 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C13 | |
8 conjugacy classes of subgroups.
585 conjugacy classes — view the full character table.
| maximal subgroup of | C13×#11765919, #28415387, #28415388, … |
| maximal normal subgroup of | C13×#11765919, #28415387, #28415388, … |
| maximal quotient of | C13×#11765917, C3×C13×C127⋊C3, C13×C22⋊(C127⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4953, 2);