Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C24×#11761640 |
| unambiguous semidirect product | D269⋊(C23×C4) |
| Fitting, socle | C24×C269 ⋊ C4 |
| derived, Sylow | C269 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | #11761640 |
| commutator, hypocenter | C269 | C24×C4 |
| Frattini | C1 | G |
| Fitting, socle | C24×C269 | C4 |
| prime radical | C24×D269 | C2 |
| cosocle | D269 | C25 |
| LCS | G ▷ C269 | |
| UCS | C1 ◁ C24 | |
1362 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4304 |
1136 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46826058 |
| maximal normal subgroup of | #46826058 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1630);