Finite Group DatabasebetaFinite Group Databasebeta| order | 33620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C412 ⋊ C4×C5 |
| Hall | #22554261 ⋊ C4 |
| Hall | #20269609 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C412 | C4×C5 |
| prime radical | #30681140 | C2 |
| cosocle | C41⋊D41 | C2×C5 |
| LCS | G ▷ C412 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 82 |
| transitive degree | μt(G) = 82 |
A minimal faithful permutation representation — 2 generators on 82 points:
(1,2)(3,16,24,63,57,6,10,33,36,62,4,23,17,32,46,9,7,15,47,77)(5,29,20,27,79,12,30,11,53,44,14,42,26,21,66,19,13,8,43,55)(18,68,74,75,28,39,51,54,41,56,25,78,58,73,22,50,40,80,52,45)(31,76,67,70,65,48,81,37,61,72,60,71,35,69,34,38,59,49,82,64);(2,15,66,78,23,13,61,45,53,26,32,80,39,75,59,60,6,35,62,65,14,5,34,77,67,9,31,81,73,50,54,63,20,43,56,82,30,16,68,79,33)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^10,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, 53);