Finite Group DatabasebetaFinite Group Databasebeta| order | 15582 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C53⋊#64418 |
| Fitting, socle, Hall | C72×C53 ⋊ D3 |
| derived, Hall | C53×#3862 ⋊ C2 |
| Hall | #3862 ⋊ D53 |
| Sylow | C53 ⋊ #64418 |
| Sylow | C72 ⋊ D159 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C53×#3862 | C2 |
| Fitting, socle | C72×C53 | D3 |
| LCS | G ▷ C53×#3862 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 742 |
Polycyclic presentation:
2,3,53,7^2|b^a=b^2,c^a=c^52,d^a=d^2e^3,e^a=d^6e^5,d^b=d^4e^4,e^b=e^2514 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#64418, #64418⋊D53, #44528394, … |
| maximal normal subgroup of | D53×#64418, #64418⋊D53, #44528394, … |
| maximal quotient of | #44528368, C2×C53⋊#64418 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15582, 32);