Finite Group DatabasebetaFinite Group Databasebeta| order | 23716 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C121 · Schur multiplier (H2) = C7 |
| direct product | C121×#5997 |
| Fitting, Hall | C72×C121 ⋊ C4 |
| derived, Sylow | C72 ⋊ C4×C121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C121 | #5997 |
| commutator, hypocenter | C72 | C4×C121 |
| Frattini | C11 | C11×#5997 |
| Fitting | C72×C121 | C4 |
| socle | C72×C11 | C4×C11 |
| prime radical, cosocle | C11×C7⋊D7 | C2×C11 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C121 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1694 |
1936 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23716, 28);