Finite Group DatabasebetaFinite Group Databasebeta| order | 36124 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#15692846 |
| Fitting, socle, derived, Hall | C11×C821 ⋊ C4 |
| Sylow | C821 ⋊ Dic11 |
| Sylow | C11 ⋊ #15692846 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C821 | C4 |
| prime radical, cosocle | C11×D821 | C2 |
| LCS | G ▷ C11×C821 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9031 |
Polycyclic presentation:
2^2,11,821|a^2=b,c^a=c^10,d^a=d^295,d^b=d^8202269 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36124, 7);