Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊Dic1911 |
| unambiguous semidirect product | C49⋊(C3⋊Dic39) |
| derived, Hall | C32×C13×C49 ⋊ C4 |
| Hall | C13×C49 ⋊ C3⋊Dic3 |
| Hall | C32×C49 ⋊ Dic13 |
| Hall | C32×C13 ⋊ Dic49 |
| Sylow | C49 ⋊ C3⋊Dic39 |
| Sylow | C13 ⋊ C3⋊Dic147 |
| Sylow | C32 ⋊ Dic637 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊D1911 |
| commutator, hypocenter | C32×C13×C49 | C4 |
| Frattini | C2×C7 | C3⋊D273 |
| Fitting, cosocle | C2×C32×C13×C49 | C2 |
| socle, prime radical | C2×C32×C7×C13 | D7 |
| LCS | G ▷ C32×C13×C49 | |
| UCS | C1 ◁ C2 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22932 |
Polycyclic presentation:
2,3^2,7,13,2,7|a^2=f,d^7=g^6,b^a=b^2,c^a=c^2,d^a=d^6g,e^a=e^12,g^a=g^65736 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 124);