Finite Group DatabasebetaFinite Group Databasebeta| order | 3392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C42×C53 ⋊ C4 |
| Sylow | C53 ⋊ #384 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#6157 |
| commutator, socle | C22×C53 | C22×C4 |
| Fitting | C42×C53 | C4 |
| prime radical, cosocle | C22×D53 | C23 |
| hypercenter | C42 | #6157 |
| hypocenter | C53 | #384 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C42 | |
186 conjugacy classes of subgroups.
| transitive degree | μt(G) = 848 |
Polycyclic presentation:
2^6,53|a^2=f,b^2=d,c^2=e,b^a=bd,c^a=ce,g^a=g^30,g^f=g^52236 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3392, 1495);