Finite Group DatabasebetaFinite Group Databasebeta| order | 700 |
| isoclinism | isoclinic class of #1042 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#1042 |
| Fitting, socle, Hall | C52×C7 ⋊ C4 |
| derived, Sylow | C52 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #1042 |
| commutator, hypocenter | C52 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7 | C4 |
| prime radical | C5×C7×D5 | C2 |
| cosocle | C5×D5 | C2×C7 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C7 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 140 |
91 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1042, C7×D5×AGL(1,𝔽5), #1042⋊D7, … |
| maximal normal subgroup of | D7×#1042, C7×D5×AGL(1,𝔽5), #1042⋊D7, … |
| maximal quotient of | C7×#6032, C2×C7×#1042, C3×C7×#1042, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(700, 24);