Finite Group DatabasebetaFinite Group Databasebeta| order | 15372 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | #13046197⋊A4 |
| Fitting, socle, derived, Hall | C22×C7×C61 ⋊ C32 |
| Hall | C7×C61 ⋊ C3×A4 |
| Hall | C22×C61 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C61 ⋊ A4×ΓL(1,𝔽8) |
| Hall | C22×C7 ⋊ C3×C61⋊C3 |
| Sylow | C7 ⋊ A4×C61⋊C3 |
| Sylow | C22 ⋊ ΓL(1,𝔽8)×C61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C7×C61 | C32 |
| LCS | G ▷ C22×C7×C61 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1708 |
Polycyclic presentation:
3^2,2^2,7,61|e^a=e^2,f^a=f^47,c^b=cd,d^b=c,e^b=e^2260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15372, 184);