Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊(C7⋊(C9⋊#261)) |
| unambiguous semidirect product | C9⋊(C7⋊(C7⋊#261)) |
| Fitting, derived, Hall | C72×C9×C13 ⋊ C4 |
| Hall | C72×C13 ⋊ Dic9 |
| Hall | C72×C9 ⋊ #261 |
| Hall | C9×C13 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ C9⋊#261 |
| Sylow | C13 ⋊ C7⋊Dic63 |
| Sylow | C9 ⋊ C7⋊(C7⋊#261) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C72×C9×C13 | C4 |
| Frattini | C3 | C3⋊(C7⋊(C7⋊#261)) |
| socle | C3×C72×C13 | Dic3 |
| prime radical | C3×C72×D13 | D3 |
| cosocle | C72×C9×D13 | C2 |
| LCS | G ▷ C72×C9×C13 | |
| UCS | C1 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5733 |
Polycyclic presentation:
2^2,3,7^2,13,3|a^2=b,c^3=g^2,c^a=c^2g,d^a=d^6,e^a=e^6,f^a=f^5,g^a=g^2,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, 523);