Finite Group DatabasebetaFinite Group Databasebeta| order | 3392 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C16×C53 ⋊ C4 |
| Sylow | C53 ⋊ #346 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×#6157 |
| commutator, socle | C2×C53 | C4×C8 |
| Fitting | C16×C53 | C4 |
| prime radical | C2×D53 | C2×C8 |
| cosocle | C8×D53 | C22 |
| hypercenter | C16 | #6157 |
| hypocenter | C53 | #346 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C8 ◁ C16 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 848 |
Polycyclic presentation:
2^6,53|a^2=c,b^2=d,c^2=e,e^2=f,b^a=bf,g^b=g^30,g^d=g^52248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3392, 1436);