Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C24×#11764049 |
| Fitting, socle | C24×C137 ⋊ C8 |
| derived, Sylow | C137 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | #11764049 |
| commutator, hypocenter | C137 | C24×C8 |
| Frattini | C1 | G |
| Fitting, socle | C24×C137 | C8 |
| prime radical | C24×D137 | C4 |
| cosocle | #10587739 | C25 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C24 | |
1976 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2192 |
400 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 21766);