Finite Group DatabasebetaFinite Group Databasebeta| order | 33620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #30681142⋊C2 |
| unambiguous semidirect product | #30681143⋊C2 |
| unambiguous semidirect product | #30681144⋊C2 |
| Fitting, socle, derived, Sylow | C412 ⋊ C22×C5 |
| Hall | #22554262 ⋊ 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 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 82 |
| transitive degree | μt(G) = 410 |
A minimal faithful permutation representation — 2 generators on 82 points:
(2,6,7,23,27,3,4,12,14,22)(5,19,20,25,26,9,10,34,13,36)(8,31,32,33,21,16,17,41,18,11)(15,38,39,24,37,29,30,40,28,35)(42,43,49,71,65)(44,54,47,60,82)(45,56,76,63,77)(46,48,67,80,66)(50,70,69,51,75)(52,58,81,53,73)(55,64,59,61,72)(57,68,62,78,74);(1,2,5,11,22,34,37,41,36,25,4,8,18,31,39,38,14,28,7,15,10,19,29,12,24,23,30,40,17,33,16,6,13,26,32,35,20,27,21,9,3)(43,44)(45,47)(46,50)(48,53)(49,57)(51,60)(52,56)(54,64)(55,63)(58,69)(59,72)(61,74)(62,68)(65,66)(67,78)(70,80)(71,77)(73,82)(75,81)(76,79)Polycyclic presentation:
2^2,5,41^2|e^a=e^40,d^b=d^40,d^c=d^10,e^c=e^18116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33620, 63);