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 | #20269608 ⋊ 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 | |
264 conjugacy classes of subgroups.
| minimal degree | μ(G) = 82 |
| transitive degree | μt(G) = 1681 |
A minimal faithful permutation representation — 3 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)(43,48,53,67,74,44,51,55,59,66,46,57,50,54,70,49,45,47,65,80)(52,73,72,76,69,61,77,60,64,81,63,82,58,79,56,75,62,71,78,68);(42,43,47,56,70,80,82,72,57,49,45,52,64,77,68,79,59,75,50,60,54,67,71,53,61,65,76,81,62,78,63,51,44,48,58,73,66,74,69,55,46);(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)Polycyclic presentation:
2,5,2,41^2|a^2=c,d^a=d^32,e^a=e^32,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, 52);