Finite Group DatabasebetaFinite Group Databasebeta| order | 23010 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C59 · Schur multiplier (H2) = C1 |
| direct product | C3×C59×D65 |
| unambiguous semidirect product | C5⋊(C3×D13×C59) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C59 | D65 |
| commutator, cosocle, hypocenter | C5×C13 | C2×C3×C59 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C13×C59 | C2 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C3×C59 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11505 |
6018 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23010, 8);