Finite Group DatabasebetaFinite Group Databasebeta| order | 27830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C5⋊(C11⋊D253) |
| unambiguous semidirect product | C11⋊D1265 |
| unambiguous semidirect product | C23⋊(C5⋊(C11⋊D11)) |
| Fitting, socle, derived, Hall | C5×C112×C23 ⋊ C2 |
| Hall | C112×C23 ⋊ D5 |
| Hall | C5×C112 ⋊ D23 |
| Sylow | C112 ⋊ D115 |
| Hall | C5×C23 ⋊ C11⋊D11 |
| Sylow | C23 ⋊ C5⋊(C11⋊D11) |
| Sylow | C5 ⋊ C11⋊D253 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C112×C23 | C2 |
| LCS | G ▷ C5×C112×C23 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13915 |
Polycyclic presentation:
2,5,11^2,23|b^a=b^4,c^a=c^10,d^a=d^10,e^a=e^226959 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27830, 70);