Finite Group DatabasebetaFinite Group Databasebeta| order | 24210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C32×C5×D269 |
| unambiguous semidirect product | C269⋊(C2×C32×C5) |
| Fitting, socle, Hall | C32×C5×C269 ⋊ C2 |
| derived, Sylow | C269 ⋊ C2×C32×C5 |
| Hall | C32×C269 ⋊ C2×C5 |
| Hall | C5×C269 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5 | D269 |
| commutator, cosocle, hypocenter | C269 | C2×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C269 | C2 |
| LCS | G ▷ C269 | |
| UCS | C1 ◁ C32×C5 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12105 |
6120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24210, 10);