Finite Group DatabasebetaFinite Group Databasebeta| order | 27002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C587 · Schur multiplier (H2) = C1 |
| direct product | D23×C587 |
| unambiguous semidirect product | C23⋊(C2×C587) |
| Fitting, socle, Hall | C23×C587 ⋊ C2 |
| derived, Sylow | C23 ⋊ C2×C587 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C587 | D23 |
| commutator, cosocle, hypocenter | C23 | C2×C587 |
| Frattini | C1 | G |
| Fitting, socle | C23×C587 | C2 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C587 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13501 |
7631 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27002, 1);