Finite Group DatabasebetaFinite Group Databasebeta| order | 33620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C5×C1681 ⋊ C4 |
| Sylow | C1681 ⋊ Dic5 |
| Sylow | C5 ⋊ #20269599 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C1681 | C4 |
| Frattini | C41 | #11717964 |
| socle | C5×C41 | #4223 |
| prime radical, cosocle | C5×D1681 | C2 |
| LCS | G ▷ C5×C1681 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8405 |
Polycyclic presentation:
2^2,5,41^2|a^2=b,d^41=e^32,c^a=c^4,d^a=d^9e,e^a=e^9,d^b=d^40e^9,e^b=e^402108 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33620, 16);