Finite Group DatabasebetaFinite Group Databasebeta| order | 15522 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#21441030 |
| Fitting, socle, Hall | C2×C13×C199 ⋊ C3 |
| derived, Hall | C13×C199 ⋊ C2×C3 |
| Hall | C2×C199 ⋊ C13⋊C3 |
| Sylow | C199 ⋊ C2×C13⋊C3 |
| Hall | C2×C13 ⋊ C199⋊C3 |
| Sylow | C13 ⋊ C2×C199⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #21441030 |
| commutator, cosocle, hypocenter | C13×C199 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C199 | C3 |
| LCS | G ▷ C13×C199 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5174 |
1730 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#21441030, #44526802, #44526806, … |
| maximal normal subgroup of | C4×#21441030, #44526802, #44526806, … |
| maximal quotient of | C4×#21441030, C22×#21441030 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15522, 5);