Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(C49⋊#261) |
| unambiguous semidirect product | C49⋊(C9⋊#261) |
| Fitting, derived, Hall | C9×C13×C49 ⋊ C4 |
| Hall | C13×C49 ⋊ Dic9 |
| Hall | C9×C49 ⋊ #261 |
| Hall | C9×C13 ⋊ Dic49 |
| Sylow | C49 ⋊ C9⋊#261 |
| Sylow | C13 ⋊ Dic441 |
| Sylow | C9 ⋊ C49⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C13×C49 | C4 |
| Frattini | C3×C7 | C3⋊(C7⋊#261) |
| socle | C3×C7×C13 | Dic21 |
| prime radical | C3×C7×D13 | D21 |
| cosocle | C9×D13×C49 | C2 |
| LCS | G ▷ C9×C13×C49 | |
| UCS | C1 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5733 |
Polycyclic presentation:
2^2,3,7,13,3,7|a^2=b,c^3=f^2,d^7=g^6,c^a=c^2f,d^a=d^6g,e^a=e^8,f^a=f^2,g^a=g^6,e^b=e^121767 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 53);