Finite Group DatabasebetaFinite Group Databasebeta| order | 23217 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×C109⋊C3 |
| unambiguous semidirect product | C109⋊(C3×C71) |
| unambiguous semidirect product | (C71×C109)⋊C3 |
| Fitting, socle, Hall | C71×C109 ⋊ C3 |
| derived, Sylow | C109 ⋊ C3×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | C109⋊C3 |
| commutator, cosocle, hypocenter | C109 | C3×C71 |
| Frattini | C1 | G |
| Fitting, socle | C71×C109 | C3 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C71 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7739 |
2769 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23217, 1);