Finite Group DatabasebetaFinite Group Databasebeta| order | 23310 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×D5×#66526 |
| unambiguous semidirect product | C5⋊(C2×C7×#66526) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D5×#66526 |
| commutator, hypocenter | C5×C37 | C2×C7×C9 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C37 | C2×C9 |
| prime radical | C7×D5×C37⋊C3 | C3 |
| cosocle | C5×C37⋊C3 | C2×C3×C7 |
| LCS | G ▷ C5×C37 | |
| UCS | C1 ◁ C7 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1295 |
364 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23310, 63);