Finite Group DatabasebetaFinite Group Databasebeta| order | 1400 |
| isoclinism | isoclinic class of D52×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D52×D7 |
| unambiguous semidirect product | (C5×D5×D7)⋊C2 |
| unambiguous semidirect product | (D7×C5⋊D5)⋊C2 |
| unambiguous semidirect product | (D5×D35)⋊C2 |
| Fitting, socle, derived, Hall | C52×C7 ⋊ C23 |
| Sylow | C52 ⋊ C22×D7 |
| Sylow | C7 ⋊ C2×D52 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C7 | C23 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 | |
148 conjugacy classes of subgroups.
| transitive degree | μt(G) = 70 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | D52×AGL(1,𝔽7), D7×D5⋊AGL(1,𝔽5), #72225761, … |
| maximal normal subgroup of | D52×AGL(1,𝔽7), D7×D5⋊AGL(1,𝔽5), C2×D52×D7, … |
| maximal quotient of | #72225761, D7×#6036, C2×D52×D7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1400, 133);