Finite Group DatabasebetaFinite Group Databasebeta| order | 33620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C41 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C412 ⋊ C4×C5 |
| Hall | #22554263 ⋊ C4 |
| Hall | #20269609 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C412 | C4×C5 |
| prime radical | #30681146 | C2 |
| cosocle | C41⋊D41 | C2×C5 |
| LCS | G ▷ C412 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 82 |
| transitive degree | μt(G) = 410 |
A minimal faithful permutation representation — 2 generators on 82 points:
(2,7,12,26,33,3,10,14,18,25,5,16,9,13,29,8,4,6,24,39)(11,32,31,35,28,20,36,19,23,40,22,41,17,38,15,34,21,30,37,27)(43,48,64,47,50,44,52,73,54,61,46,59,51,56,62,49,45,58,68,55)(53,79,77,76,63,66,72,74,82,65,57,81,70,60,78,71,67,69,75,80);(1,2,6,15,29,39,41,31,16,8,4,11,23,36,27,38,18,34,9,19,13,26,30,12,20,24,35,40,21,37,22,10,3,7,17,32,25,33,28,14,5)(42,43,47,57,52,48,60,77,61,44,50,63,67,75,66,81,51,65,54,69,73,58,74,68,80,64,79,71,82,72,78,62,49,55,70,76,59,45,53,56,46)Polycyclic presentation:
2,5,2,41^2|a^2=c,d^a=d^32,e^a=e^9,d^b=d^10,e^b=e^37,d^c=d^40,e^c=e^40104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33620, 68);