Finite Group DatabasebetaFinite Group Databasebeta| order | 28365 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C31×C61 ⋊ C3×C5 |
| Hall | #22628161 ⋊ C3 |
| Hall | C31×C61⋊C3 ⋊ C5 |
| Hall | C61⋊C3 ⋊ ΓL(1,𝔽32) |
| Sylow | C61 ⋊ C3×ΓL(1,𝔽32) |
| Sylow | C31 ⋊ (C61⋊C3)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C61 | C3×C5 |
| LCS | G ▷ C31×C61 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1891 |
Polycyclic presentation:
3,5,31,61|d^a=d^47,c^b=c^16,d^b=d^58157 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28365, 16);