Finite Group DatabasebetaFinite Group Databasebeta| order | 23716 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C11⋊Dic539 |
| unambiguous semidirect product | C49⋊(C11⋊Dic11) |
| derived, Hall | C112×C49 ⋊ C4 |
| Sylow | C112 ⋊ Dic49 |
| Sylow | C49 ⋊ C11⋊Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C11⋊D539 |
| commutator, hypocenter | C112×C49 | C4 |
| Frattini | C2×C7 | C7⋊(C11⋊D11) |
| Fitting, cosocle | C2×C112×C49 | C2 |
| socle, prime radical | C2×C7×C112 | D7 |
| LCS | G ▷ C112×C49 | |
| UCS | C1 ◁ C2 | |
126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23716 |
Polycyclic presentation:
2,7,11^2,2,7|a^2=e,b^7=f^6,b^a=b^6f,c^a=c^10,d^a=d^10,f^a=f^65932 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23716, 21);