Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊(C49⋊#261)) |
| unambiguous semidirect product | C49⋊(C3⋊(C3⋊#261)) |
| Fitting, derived, Hall | C32×C13×C49 ⋊ C4 |
| Hall | C13×C49 ⋊ C3⋊Dic3 |
| Hall | C32×C49 ⋊ #261 |
| Hall | C32×C13 ⋊ Dic49 |
| Sylow | C49 ⋊ C3⋊(C3⋊#261) |
| Sylow | C13 ⋊ C3⋊Dic147 |
| Sylow | C32 ⋊ C49⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C32×C13×C49 | C4 |
| Frattini | C7 | C3⋊(C3⋊(C7⋊#261)) |
| socle | C32×C7×C13 | Dic7 |
| prime radical | C32×C7×D13 | D7 |
| cosocle | C32×D13×C49 | C2 |
| LCS | G ▷ C32×C13×C49 | |
| UCS | C1 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5733 |
Polycyclic presentation:
2^2,3^2,7,13,7|a^2=b,e^7=g^6,c^a=c^2,d^a=d^2,e^a=e^6g,f^a=f^5,g^a=g^6,f^b=f^121767 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 226);