Finite Group DatabasebetaFinite Group Databasebeta| order | 3392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×Q8×C53 ⋊ C4 |
| Sylow | C53 ⋊ #410 |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 848 |
Polycyclic presentation:
2^6,53|a^2=e,c^2=f,b^a=bd,d^a=df,g^a=g^30,e^b=ef,g^b=g^52,g^c=g^52,g^e=g^52152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3392, 1530);