Finite Group DatabasebetaFinite Group Databasebeta| order | 27830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D1265 |
| unambiguous semidirect product | C5⋊(C11×D253) |
| unambiguous semidirect product | C11⋊(C11×D115) |
| Fitting, socle, Hall | C5×C112×C23 ⋊ C2 |
| derived | C5×C11×C23 ⋊ C2×C11 |
| Hall | C112×C23 ⋊ D5 |
| Hall | C5×C112 ⋊ D23 |
| Sylow | C112 ⋊ D115 |
| Hall | C5×C23 ⋊ C11×D11 |
| Sylow | C23 ⋊ C11×D55 |
| Sylow | C5 ⋊ C11×D253 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D1265 |
| commutator, cosocle, hypocenter | C5×C11×C23 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C112×C23 | C2 |
| LCS | G ▷ C5×C11×C23 | |
| UCS | C1 ◁ C11 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2530 |
6974 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27830, 68);