Finite Group DatabasebetaFinite Group Databasebeta| order | 27830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×#11925895 |
| Fitting, socle, Hall | C112×C23 ⋊ C2×C5 |
| derived, Sylow | C112 ⋊ C2×C5×C23 |
| Hall | C23×#10597243 ⋊ C2 |
| Hall | C11×D11×C23 ⋊ C5 |
| Hall | #10597243 ⋊ C2×C23 |
| Hall | C11×D11 ⋊ C5×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #11925895 |
| commutator, cosocle, hypocenter | C112 | C2×C5×C23 |
| Frattini | C1 | G |
| Fitting, socle | C112×C23 | C2×C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C23 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 506 |
575 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27830, 42);