Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C215 |
| direct product | C25×#10587739 |
| unambiguous semidirect product | D137⋊(C24×C4) |
| Fitting, socle | C25×C137 ⋊ C4 |
| derived, Sylow | C137 ⋊ C25×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | #10587739 |
| commutator, hypocenter | C137 | C25×C4 |
| Frattini | C1 | G |
| Fitting, socle | C25×C137 | C4 |
| prime radical | C25×D137 | C2 |
| cosocle | D137 | C26 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C25 | |
10552 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4384 |
1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 21507);