Finite Group DatabasebetaFinite Group Databasebeta| order | 23716 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊Dic847 |
| unambiguous semidirect product | C121⋊(C7⋊Dic7) |
| derived, Hall | C72×C121 ⋊ C4 |
| Sylow | C121 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ Dic121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C7⋊D847 |
| commutator, hypocenter | C72×C121 | C4 |
| Frattini | C2×C11 | C7⋊D77 |
| Fitting, cosocle | C2×C72×C121 | C2 |
| socle, prime radical | C2×C72×C11 | D11 |
| LCS | G ▷ C72×C121 | |
| UCS | C1 ◁ C2 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23716 |
Polycyclic presentation:
2,7^2,11,2,11|a^2=e,d^11=f^10,b^a=b^6,c^a=c^6,d^a=d^10f,f^a=f^105932 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23716, 15);