Finite Group DatabasebetaFinite Group Databasebeta| order | 15582 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C53⋊#64423 |
| Fitting, socle, derived, Hall | C72×C53 ⋊ C2×C3 |
| Hall | C53×#3861 ⋊ C2 |
| Hall | C7×D371 ⋊ C3 |
| Hall | #3861 ⋊ D53 |
| Sylow | C53 ⋊ #64423 |
| Sylow | C72 ⋊ C3×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C53 | C2×C3 |
| LCS | G ▷ C72×C53 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 742 |
Polycyclic presentation:
2,3,7^2,53|c^a=c^6,e^a=e^52,c^b=c^2,d^b=d^2511 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#64423, #64423⋊D53, #64424⋊D53, … |
| maximal normal subgroup of | D53×#64423, #64423⋊D53, #64424⋊D53, … |
| maximal quotient of | #44528358, C2×C53⋊#64423 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15582, 22);