Finite Group DatabasebetaFinite Group Databasebeta| order | 1288 |
| isoclinism | isoclinic class of D7×D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D161⋊C4 |
| derived, Hall | C7×C23 ⋊ C2×C4 |
| Sylow | C23 ⋊ C4×D7 |
| Sylow | C7 ⋊ C4×D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D7×D23 |
| commutator, hypocenter | C7×C23 | C2×C4 |
| Fitting, socle, cosocle | C2×C7×C23 | C22 |
| prime radical | C2×D161 | C2 |
| LCS | G ▷ C7×C23 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 644 |
Polycyclic presentation:
2^3,7,23|a^2=c,b^2=c,e^a=e^22,d^b=d^6130 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1288, 7);