Finite Group DatabasebetaFinite Group Databasebeta| order | 2624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C41 ⋊ C4 |
| Sylow | C41 ⋊ AΣL(1,𝔽16) |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 328 |
Polycyclic presentation:
2^6,41|a^2=d,b^a=bc,c^a=ce,e^a=ef,g^a=g^32,d^b=de,g^b=g^40,d^c=df,g^d=g^40113 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2624, 1450);