Finite Group DatabasebetaFinite Group Databasebeta| order | 4953 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C127 ⋊ C3 |
| Sylow | C127 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ C127⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C127 | C3 |
| LCS | G ▷ C13×C127 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
3,13,127|b^a=b^9,c^a=c^19553 conjugacy classes — view the full character table.
| maximal subgroup of | C13⋊C3×C127⋊C3, C3×#19097154, C22⋊#19097154, … |
| maximal normal subgroup of | C13⋊C3×C127⋊C3, C3×#19097154, C5×#19097154, … |
| maximal quotient of | #28415384, C3×#19097154, C22⋊#19097154, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4953, 4);