Finite Group DatabasebetaFinite Group Databasebeta| order | 27830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊#11925898 |
| Fitting, socle, derived, Hall | C112×C23 ⋊ C2×C5 |
| Hall | C23×#10597244 ⋊ C2 |
| Hall | C11×D253 ⋊ C5 |
| Hall | #10597244 ⋊ D23 |
| Sylow | C112 ⋊ C5×D23 |
| Sylow | C23 ⋊ #11925898 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C23 | C2×C5 |
| LCS | G ▷ C112×C23 | |
| UCS | C1 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2530 |
Polycyclic presentation:
2,5,11^2,23|c^a=c^10,e^a=e^22,c^b=c^4,d^b=d^5344 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27830, 46);