Finite Group DatabasebetaFinite Group Databasebeta| order | 3392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D16×C53 ⋊ C2 |
| Sylow | C53 ⋊ D32 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #13133158 |
| commutator, cosocle | C16×C53 | C22 |
| Frattini | C16 | C2×D53 |
| Fitting | D16×C53 | C2 |
| socle | C2×C53 | D16 |
| hypercenter | D16 | D53 |
| hypocenter | C53 | D32 |
| LCS | G ▷ C16×C53 ▷ C8×C53 ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ D16 | |
34 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^6,53|c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,c^b=cd,d^b=de,e^b=ef,g^b=g^52305 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3392, 384);