Finite Group DatabasebetaFinite Group Databasebeta| order | 33620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #30681136⋊C2 |
| Fitting, socle, Sylow | C412 ⋊ C2×D5 |
| derived, Hall | #22554263 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #22554263 | C22 |
| Fitting, socle | C412 | C2×D5 |
| LCS | G ▷ #22554263 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 82 |
Polycyclic presentation:
2^2,5,41^2|d^a=d^40,e^a=e^40,c^b=c^4,d^b=e,e^b=d,d^c=d^10,e^c=e^37152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33620, 44);