Finite Group DatabasebetaFinite Group Databasebeta| order | 33424 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C2089 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #30660060 |
| commutator, hypocenter | C2089 | C16 |
| Fitting, socle, prime radical | C2×C2089 | C8 |
| cosocle | #30660058 | C2 |
| LCS | G ▷ C2089 | |
| UCS | C1 ◁ C2 | |
10 conjugacy classes of subgroups.
| transitive degree | μt(G) = 33424 |
Polycyclic presentation:
2^4,2089|a^2=b,b^2=c,c^2=d,e^a=e^1517,e^b=e^1300,e^c=e^2088538 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33424, 52);