Finite Group DatabasebetaFinite Group Databasebeta| order | 2656 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #41×C83 ⋊ C2 |
| Sylow | C83 ⋊ AGL(1,ℤ/8) |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×C22⋊D83 |
| commutator, cosocle | C4×C83 | C23 |
| Frattini | C4 | C22×D83 |
| Fitting | #41×C83 | C2 |
| socle | C2×C83 | C2×D4 |
| hypercenter | #41 | D83 |
| hypocenter | C83 | AGL(1,ℤ/8) |
| LCS | G ▷ C4×C83 ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #41 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 664 |
Polycyclic presentation:
2^5,83|d^2=e,b^a=bd,c^a=ce,d^a=de,d^b=de,f^b=f^82421 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2656, 171);