Finite Group DatabasebetaFinite Group Databasebeta| order | 3392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #519 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D53 |
| commutator | C2×C53 | C23×C4 |
| Fitting | #117×C53 | C2 |
| socle, cosocle | C22×C53 | C24 |
| prime radical | C23×C53 | C23 |
| hypercenter | #117 | D53 |
| hypocenter | C53 | #519 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ #117 | |
266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^6,53|a^2=f,b^2=e,c^2=e,b^a=be,d^a=de,c^b=ce,g^c=g^52554 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3392, 1026);