Finite Group DatabasebetaFinite Group Databasebeta| order | 1288 |
| isoclinism | isoclinic class of D161 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(C23⋊C8) |
| unambiguous semidirect product | C23⋊(C7⋊C8) |
| derived, Hall | C7×C23 ⋊ C8 |
| Sylow | C23 ⋊ C7⋊C8 |
| Sylow | C7 ⋊ C23⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D161 |
| commutator, hypocenter | C7×C23 | C8 |
| Fitting, cosocle | C4×C7×C23 | C2 |
| socle, prime radical | C2×C7×C23 | C4 |
| LCS | G ▷ C7×C23 | |
| UCS | C1 ◁ C4 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 1288 |
Polycyclic presentation:
2^3,7,23|a^2=b,b^2=c,d^a=d^6,e^a=e^22328 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1288, 3);