Finite Group DatabasebetaFinite Group Databasebeta| order | 2536 |
| isoclinism | isoclinic class of D317 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×Dic317 |
| derived, Sylow | C317 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D317 |
| commutator, hypocenter | C317 | C2×C4 |
| Frattini | C2 | C2×D317 |
| Fitting, socle, prime radical | C22×C317 | C2 |
| cosocle | C2×C317 | C22 |
| LCS | G ▷ C317 | |
| UCS | C1 ◁ C22 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2536 |
640 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2536, 8);