Finite Group DatabasebetaFinite Group Databasebeta| order | 23716 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7×C11 |
| unambiguous semidirect product | C7⋊(C7⋊#92150) |
| Fitting, socle, derived, Hall | C72×C112 ⋊ C4 |
| Sylow | C112 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ #92150 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C112 | C4 |
| prime radical, cosocle | C72×C11⋊D11 | C2 |
| LCS | G ▷ C72×C112 | |
| UCS | C1 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1078 |
Polycyclic presentation:
2^2,7^2,11^2|a^2=b,c^a=c^6,d^a=d^6,e^a=e^8f^7,f^a=e^8f^3,e^b=e^10,f^b=f^101522 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23716, 76);