Finite Group DatabasebetaFinite Group Databasebeta| order | 33620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #30681140⋊C2 |
| unambiguous semidirect product | #30681141⋊C2 |
| Fitting, socle, derived, Sylow | C412 ⋊ C22×C5 |
| Hall | #22554261 ⋊ C22 |
| Hall | D412 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C412 | C22×C5 |
| LCS | G ▷ C412 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| minimal degree | μ(G) = 82 |
| transitive degree | μt(G) = 82 |
A minimal faithful permutation representation — 2 generators on 82 points:
(1,5,22,68,50,2,4,26,36,56)(3,30,70,65,46,6,16,76,35,69)(7,58,49,59,24,13,33,55,38,28)(8,61,43,41,48,17,32,51,19,54)(9,52,74,57,40,11,45,82,31,71)(10,39,72,27,42,12,18,79,23,73)(14,75,62,53,64,29,60,78,47,77)(15,81,20,63,66,34,67,25,44,80)(21,37);(1,5,8,28,42,71,64,80,38,37,7,26,36,65,74,78,31,63,14,52,18,39,45,29,44,57,62,82,35,68,22,13,21,59,66,77,40,73,24,17,4,2,3,12,19,56,49,79,70,69,16,11,15,54,47,81,60,51,33,25,32,27,23,61,20,58,43,75,67,53,48,34,9,30,46,76,72,55,50,41,10,6)Polycyclic presentation:
2^2,5,41^2|e^a=e^40,d^b=d^40,d^c=d^10,e^c=e^10116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33620, 60);