Finite Group DatabasebetaFinite Group Databasebeta| order | 15522 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C199 ⋊ C2×C3 |
| Hall | #21441030 ⋊ C2 |
| Hall | D13×C199 ⋊ C3 |
| Sylow | C199 ⋊ D13⋊C3 |
| Hall | D13 ⋊ C199⋊C3 |
| Sylow | C13 ⋊ C2×C199⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C199 | C2×C3 |
| LCS | G ▷ C13×C199 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2587 |
Polycyclic presentation:
2,3,13,199|c^a=c^12,c^b=c^3,d^b=d^92536 conjugacy classes — view the full character table.
| maximal subgroup of | #44526813, #44526815, #29509393⋊C2, … |
| maximal normal subgroup of | #44526813, #44526815, #29509393⋊C2, … |
| maximal quotient of | #44526806, C2×#29509397 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15522, 20);