Finite Group DatabasebetaFinite Group Databasebeta| order | 1400 |
| isoclinism | isoclinic class of D52⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D52⋊D7 |
| Fitting, socle, Hall | C52×C7 ⋊ D4 |
| Sylow | C52 ⋊ C22⋊D7 |
| Sylow | C7 ⋊ D52⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | C7×C5⋊D5 | C22 |
| Fitting, socle, hypocenter | C52×C7 | D4 |
| LCS | G ▷ C7×C5⋊D5 ▷ C52×C7 | |
| UCS | C1 | |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 70 |
Polycyclic presentation:
2^3,5^2,7|a^2=c,b^a=bc,d^a=d^2,e^a=e^3,f^a=f^6,d^b=e,e^b=d,d^c=d^4,e^c=e^462 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1400, 130);