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 | #20269608 ⋊ 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 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 82 |
| transitive degree | μt(G) = 205 |
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)(43,47,61,59,68,44,51,66,56,58,46,54,50,49,70,48,45,53,57,71)(52,62,73,80,77,60,74,67,82,69,65,55,78,81,63,72,64,75,79,76);(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)(42,43,47,55,61,66,78,72,59,48,56,69,81,67,64,79,68,77,45,52,58,71,65,51,63,70,82,74,75,80,76,57,44,49,60,73,53,50,62,54,46)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^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, 59);