Finite Group DatabasebetaFinite Group Databasebeta| order | 3392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #386 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D53 |
| commutator | C22×C53 | C22×C4 |
| Fitting, prime radical | C22×D4×C53 | C2 |
| socle, cosocle | C23×C53 | C23 |
| hypercenter | C22×D4 | D53 |
| hypocenter | C53 | #386 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
286 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^6,53|a^2=f,b^2=df,b^a=bd,c^a=ce,g^a=g^52,g^b=g^52548 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3392, 429);