Finite Group DatabasebetaFinite Group Databasebeta| order | 29150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C53⋊(D11⋊C25) |
| unambiguous semidirect product | (C11⋊C25)⋊D53 |
| unambiguous semidirect product | D583⋊C25 |
| derived, Hall | C11×C53 ⋊ C2×C25 |
| Hall | C53×C11⋊C25 ⋊ C2 |
| Hall | D583 ⋊ C25 |
| Hall | C11⋊C25 ⋊ D53 |
| Sylow | C53 ⋊ D11⋊C25 |
| Sylow | C11 ⋊ C25×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | C53⋊AGL(1,𝔽11) |
| commutator, hypocenter | C11×C53 | C2×C25 |
| Fitting, socle, cosocle | C5×C11×C53 | C2×C5 |
| prime radical | C5×D583 | C5 |
| LCS | G ▷ C11×C53 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14575 |
Polycyclic presentation:
2,5,11,53,5|b^5=e,c^a=c^10,d^a=d^52,c^b=c^4965 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29150, 12);