Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊#19153199 |
| derived, Hall | C22×C72×C13 ⋊ C9 |
| Hall | C72×C13 ⋊ C22⋊C9 |
| Hall | C22×C72 ⋊ C13⋊C9 |
| Hall | C22×C13 ⋊ #89204 |
| Sylow | C72 ⋊ C22⋊(C13⋊C9) |
| Sylow | C13 ⋊ C22⋊#89204 |
| Sylow | C22 ⋊ #19153199 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊#14274262 |
| commutator, hypocenter | C22×C72×C13 | C9 |
| Fitting, socle, prime radical, cosocle | C22×C3×C72×C13 | C3 |
| LCS | G ▷ C22×C72×C13 | |
| UCS | C1 ◁ C3 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11466 |
Polycyclic presentation:
3,2^2,7^2,13,3|a^3=g,b^a=c,c^a=bc,d^a=d^4,e^a=e^4,f^a=f^32556 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 544);