Finite Group DatabasebetaFinite Group Databasebeta| order | 700 |
| isoclinism | isoclinic class of C5⋊D35 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C7⋊#1039 |
| derived, Hall | C52×C7 ⋊ C4 |
| Sylow | C52 ⋊ Dic7 |
| Sylow | C7 ⋊ #1039 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊D35 |
| commutator, hypocenter | C52×C7 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C52×C7 | C2 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 700 |
Polycyclic presentation:
2^2,5^2,7|a^2=b,c^a=c^4,d^a=d^4,e^a=e^6178 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1039, Dic7×C5⋊D5, #13063776, … |
| maximal normal subgroup of | D7×#1039, Dic7×C5⋊D5, #13063776, … |
| maximal quotient of | C7⋊#6029, C2×C7⋊#1039, C3×C7⋊#1039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(700, 16);