Finite Group DatabasebetaFinite Group Databasebeta| order | 5148 |
| isoclinism | isoclinic class of #90866 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C3 |
| direct product | C11×#90866 |
| Fitting, socle, Hall | C32×C11×C13 ⋊ C4 |
| derived, Hall | C32×C13 ⋊ C4×C11 |
| Hall | C11×C13 ⋊ #157 |
| Hall | C32×C11 ⋊ #261 |
| Sylow | C13 ⋊ C11×#157 |
| Sylow | C32 ⋊ C11×#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #90866 |
| commutator, hypocenter | C32×C13 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C13 | C4 |
| LCS | G ▷ C32×C13 | |
| UCS | C1 ◁ C11 | |
40 conjugacy classes of subgroups.
363 conjugacy classes — view the full character table.
| maximal subgroup of | C11⋊C5×#90866, C5×C11×#90866, C11×#14556842, … |
| maximal normal subgroup of | C11⋊C5×#90866, C5×C11×#90866, C7×C11×#90866 |
| maximal quotient of | C5×C11×#90866, C11×#14556842, C11×#14556843, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5148, 111);