Finite Group DatabasebetaFinite Group Databasebeta| order | 33620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D205⋊D41 |
| Fitting, socle, derived, Hall | C5×C412 ⋊ C22 |
| Sylow | C412 ⋊ C2×D5 |
| Sylow | C5 ⋊ D412 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C412 | C22 |
| LCS | G ▷ C5×C412 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 410 |
Polycyclic presentation:
2^2,5,41^2|c^a=c^4,d^a=d^40,d^b=d^40,e^b=e^402168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33620, 103);