Finite Group DatabasebetaFinite Group Databasebeta| order | 23716 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C7 |
| unambiguous semidirect product | (C11⋊D11)⋊(C7⋊D7) |
| Fitting, socle, derived, Hall | C72×C112 ⋊ C22 |
| Sylow | C112 ⋊ C2×C7⋊D7 |
| Sylow | C72 ⋊ D112 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C112 | C22 |
| LCS | G ▷ C72×C112 | |
| UCS | C1 | |
300 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1078 |
Polycyclic presentation:
2^2,7^2,11^2|c^a=c^6,d^a=d^6,e^a=e^10,e^b=e^10,f^b=f^101537 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23716, 79);