Finite Group DatabasebetaFinite Group Databasebeta| order | 22396 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#14523266 |
| Fitting, socle, derived, Hall | C11×C509 ⋊ C4 |
| Sylow | C509 ⋊ Dic11 |
| Sylow | C11 ⋊ #14523266 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C509 | C4 |
| prime radical, cosocle | C11×D509 | C2 |
| LCS | G ▷ C11×C509 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5599 |
Polycyclic presentation:
2^2,11,509|a^2=b,c^a=c^10,d^a=d^208,d^b=d^5081411 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22396, 7);