Finite Group DatabasebetaFinite Group Databasebeta| order | 700 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C52×D7 |
| unambiguous semidirect product | C7⋊(C22×C52) |
| unambiguous semidirect product | (C2×C7)⋊(C2×C52) |
| Fitting, socle | C2×C52×C7 ⋊ C2 |
| derived, Sylow | C7 ⋊ C22×C52 |
| Hall | C52×C7 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52 | D7 |
| commutator, cosocle, hypocenter | C7 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C7 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C52 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 350 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D7×Dic5, C5×#63305, C5×#63306, … |
| maximal normal subgroup of | C5×D7×Dic5, C5×#63305, C5×#63306, … |
| maximal quotient of | C52×Dic14, C4×C52×D7, C52×D28, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(700, 31);