Finite Group DatabasebetaFinite Group Databasebeta| order | 23762 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C109 · Schur multiplier (H2) = C1 |
| direct product | C109×D109 |
| unambiguous semidirect product | C109⋊(C2×C109) |
| Fitting, socle, Sylow | C1092 ⋊ C2 |
| derived | C109 ⋊ C2×C109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C109 | D109 |
| commutator, cosocle, hypocenter | C109 | C2×C109 |
| Frattini | C1 | G |
| Fitting, socle | C1092 | C2 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C109 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 218 |
6104 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23762, 3);