Finite Group DatabasebetaFinite Group Databasebeta| order | 23715 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5×C17 · Schur multiplier (H2) = C3 |
| direct product | C32×C17×ΓL(1,𝔽32) |
| unambiguous semidirect product | (C32×C31)⋊(C5×C17) |
| unambiguous semidirect product | (C32×C17×C31)⋊C5 |
| Fitting, socle, Hall | C32×C17×C31 ⋊ C5 |
| derived, Sylow | C31 ⋊ C32×C5×C17 |
| Hall | C17×C31 ⋊ C32×C5 |
| Hall | C32×C31 ⋊ C5×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C17 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C32×C5×C17 |
| Frattini | C1 | G |
| Fitting, socle | C32×C17×C31 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C32×C17 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4743 |
1683 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23715, 7);