Finite Group DatabasebetaFinite Group Databasebeta| order | 24282 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D4047 |
| unambiguous semidirect product | C19⋊(C3⋊D213) |
| unambiguous semidirect product | C71⋊(C3⋊D57) |
| Fitting, socle, derived, Hall | C32×C19×C71 ⋊ C2 |
| Hall | C19×C71 ⋊ C3⋊D3 |
| Hall | C32×C71 ⋊ D19 |
| Hall | C32×C19 ⋊ D71 |
| Sylow | C71 ⋊ C3⋊D57 |
| Sylow | C19 ⋊ C3⋊D213 |
| Sylow | C32 ⋊ D1349 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C19×C71 | C2 |
| LCS | G ▷ C32×C19×C71 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12141 |
Polycyclic presentation:
2,3^2,19,71|b^a=b^2,c^a=c^2,d^a=d^18,e^a=e^706072 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24282, 36);