Finite Group DatabasebetaFinite Group Databasebeta| order | 33550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#20269514 |
| Fitting, socle, derived | C5×C11×C61 ⋊ C2×C5 |
| Hall | C5×#16809824 ⋊ C2 |
| Hall | C11×C61 ⋊ C5×D5 |
| Sylow | C61 ⋊ D5×C11⋊C5 |
| Sylow | C11 ⋊ C5⋊(D61⋊C5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C11×C61 | C2×C5 |
| LCS | G ▷ C5×C11×C61 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 3355 |
A minimal faithful permutation representation — 2 generators on 77 points:
(2,3)(4,5)(7,8,10,13,12)(9,11,15,16,14)(18,22,23,27,44,19,20,28,30,38)(21,35,36,45,60,25,26,31,53,43)(24,47,48,49,61,32,33,52,65,66)(29,34,59,67,64,41,42,50,74,55)(37,51,72,56,57,40,54,68,39,73)(46,75,69,58,76,62,63,77,71,70);(1,2,4,5,3)(6,7,9,12,8,10,14,16,11,13,15)(17,18,21,27,39,58,45,60,41,20,24,34,51,69,72,63,76,48,26,37,23,31,46,59,74,73,66,38,55,33,49,65,47,64,44,61,57,67,50,62,36,28,40,35,52,70,75,68,77,54,42,32,22,29,43,53,71,56,30,25,19)Polycyclic presentation:
2,5^2,11,61|c^a=c^4,e^a=e^60,d^b=d^4,e^b=e^9358 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33550, 69);