Finite Group DatabasebetaFinite Group Databasebeta| order | 27830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D23×#10597243 |
| unambiguous semidirect product | C23⋊(C2×#10597243) |
| Fitting, socle, derived, Hall | C112×C23 ⋊ C2×C5 |
| Hall | C23×#10597243 ⋊ C2 |
| Hall | C112×D23 ⋊ C5 |
| Sylow | C112 ⋊ C5×D23 |
| Sylow | C23 ⋊ C2×#10597243 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C23 | C2×C5 |
| LCS | G ▷ C112×C23 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2783 |
377 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27830, 39);