Finite Group DatabasebetaFinite Group Databasebeta| order | 2536 |
| isoclinism | isoclinic class of D317 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C317 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D317 |
| commutator, hypocenter | C317 | C8 |
| Fitting, cosocle | C4×C317 | C2 |
| socle, prime radical | C2×C317 | C4 |
| LCS | G ▷ C317 | |
| UCS | C1 ◁ C4 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 325 |
| transitive degree | μt(G) = 2536 |
Polycyclic presentation:
2^3,317|a^2=b,b^2=c,d^a=d^316640 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2536, 6);