Finite Group DatabasebetaFinite Group Databasebeta| order | 3392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D53⋊C32 |
| derived, Sylow | C53 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | #6157 |
| commutator, hypocenter | C53 | C2×C32 |
| Frattini | C8 | C2×#6157 |
| Fitting | C16×C53 | C4 |
| socle | C2×C53 | C2×C16 |
| prime radical | C2×D53 | C16 |
| cosocle | #11719908 | C22 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C16 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^6,53|a^2=c,c^2=d,d^2=e,e^2=f,g^a=g^30,g^b=g^52,g^c=g^52272 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3392, 1480);