Finite Group DatabasebetaFinite Group Databasebeta| order | 1400 |
| isoclinism | isoclinic class of C7⋊#1042 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#6032 |
| derived, Hall | C52×C7 ⋊ C8 |
| Sylow | C52 ⋊ C7⋊C8 |
| Sylow | C7 ⋊ #6032 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C7⋊#1042 |
| commutator, hypocenter | C52×C7 | C8 |
| Fitting, socle, prime radical | C2×C52×C7 | C4 |
| cosocle | C5×C7×Dic5 | C2 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 280 |
Polycyclic presentation:
2^3,5^2,7|a^2=b,b^2=c,d^a=d^2,e^a=e^4,f^a=f^6,d^b=d^4146 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1400, 54);