Finite Group DatabasebetaFinite Group Databasebeta| order | 23716 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7×C11 |
| unambiguous semidirect product | C7⋊(C7⋊(C11⋊Dic11)) |
| unambiguous semidirect product | C11⋊(C7⋊Dic77) |
| derived, Hall | C72×C112 ⋊ C4 |
| Sylow | C112 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ C11⋊Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C7⋊(C7⋊(C11⋊D11)) |
| commutator, hypocenter | C72×C112 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C72×C112 | C2 |
| LCS | G ▷ C72×C112 | |
| UCS | C1 ◁ C2 | |
420 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23716 |
Polycyclic presentation:
2,7^2,11^2,2|a^2=f,b^a=b^6,c^a=c^6,d^a=d^10,e^a=e^105932 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23716, 49);