Finite Group DatabasebetaFinite Group Databasebeta| order | 23310 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×C5×C7×#66526 |
| Fitting, socle, Hall | C2×C5×C7×C37 ⋊ C9 |
| derived, Sylow | C37 ⋊ C2×C5×C7×C9 |
| Hall | C5×C7×C37 ⋊ C2×C9 |
| Hall | C2×C7×C37 ⋊ C5×C9 |
| Hall | C2×C5×C37 ⋊ C7×C9 |
| Hall | C7×C37 ⋊ C2×C5×C9 |
| Hall | C5×C37 ⋊ C2×C7×C9 |
| Hall | C2×C37 ⋊ C5×C7×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C7 | #66526 |
| commutator, hypocenter | C37 | C2×C5×C7×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C7×C37 | C9 |
| prime radical | C2×C5×C7×C37⋊C3 | C3 |
| cosocle | C37⋊C3 | C2×C3×C5×C7 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2×C5×C7 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2590 |
910 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23310, 78);