Finite Group DatabasebetaFinite Group Databasebeta| order | 15582 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C53⋊(D49⋊C3) |
| unambiguous semidirect product | (C49⋊C3)⋊D53 |
| unambiguous semidirect product | D2597⋊C3 |
| Fitting, derived, Hall | C49×C53 ⋊ C2×C3 |
| Hall | C53×C49⋊C3 ⋊ C2 |
| Hall | D2597 ⋊ C3 |
| Hall | C49⋊C3 ⋊ D53 |
| Sylow | C53 ⋊ D49⋊C3 |
| Sylow | C49 ⋊ C3×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C49×C53 | C2×C3 |
| Frattini | C7 | ΓL(1,𝔽8)⋊D53 |
| socle | C7×C53 | AGL(1,𝔽7) |
| LCS | G ▷ C49×C53 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2597 |
Polycyclic presentation:
2,3,7,53,7|c^7=e^6,c^a=c^6e,d^a=d^52,e^a=e^6,c^b=c^2e^3,e^b=e^2508 conjugacy classes — view the full character table.
| maximal subgroup of | D53×D49⋊C3, C2×C53⋊(D49⋊C3) |
| maximal normal subgroup of | D53×D49⋊C3, C2×C53⋊(D49⋊C3) |
| maximal quotient of | (C49⋊C3)⋊Dic53, C2×C53⋊(D49⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15582, 12);