Finite Group DatabasebetaFinite Group Databasebeta| order | 23716 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C121⋊#5997 |
| Fitting, derived, Hall | C72×C121 ⋊ C4 |
| Sylow | C121 ⋊ #5997 |
| Sylow | C72 ⋊ Dic121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C72×C121 | C4 |
| Frattini | C11 | C11⋊#5997 |
| socle | C72×C11 | Dic11 |
| prime radical | C11×C7⋊D7 | D11 |
| cosocle | C7⋊D7×C121 | C2 |
| LCS | G ▷ C72×C121 | |
| UCS | C1 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1694 |
Polycyclic presentation:
2^2,7^2,11^2|a^2=b,e^11=f^10,c^a=c^4d^6,d^a=c^3d^3,e^a=e^10f,f^a=f^10,c^b=c^6,d^b=d^61576 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23716, 29);