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 | #22554262 ⋊ C4 |
| Hall | #20269609 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C412 | C4×C5 |
| prime radical | #30681143 | 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)(43,48,62,57,59,44,52,54,50,73,46,47,51,58,74,49,45,56,60,68)(53,55,80,77,75,65,69,78,82,76,67,63,71,81,64,72,66,70,79,61);(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)(42,43,47,55,62,56,71,65,58,44,50,61,77,70,66,79,59,75,45,53,68,73,67,52,64,74,82,69,78,81,76,60,49,57,72,80,54,51,63,48,46)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^18,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, 58);