Finite Group DatabasebetaFinite Group Databasebeta| order | 33620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | #22554263 ⋊ C4 |
| Sylow | C412 ⋊ Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #30681136 |
| commutator, hypocenter | #22554263 | C4 |
| Fitting, socle | C2×C412 | D5 |
| prime radical, cosocle | C2×#22554263 | C2 |
| LCS | G ▷ #22554263 | |
| UCS | C1 ◁ C2 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 164 |
Polycyclic presentation:
2,5,41^2,2|a^2=e,b^a=b^4,c^a=d,d^a=c,c^b=c^37,d^b=d^10464 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33620, 22);