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 | C41×C41⋊C5 ⋊ C4 |
| Hall | #20269606 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C412 | C4×C5 |
| prime radical | D41×C41⋊C5 | C2 |
| cosocle | C41×D41 | C2×C5 |
| LCS | G ▷ C412 | |
| UCS | C1 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 820 |
Polycyclic presentation:
2,5,2,41^2|a^2=c,d^a=d^32,e^a=e^40,e^b=e^10,d^c=d^40158 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33620, 51);