Finite Group DatabasebetaFinite Group Databasebeta| order | 15050 |
| isoclinism | isoclinic class of C43⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52×C7 · Schur multiplier (H2) = C5 |
| direct product | C2×C52×C43⋊C7 |
| unambiguous semidirect product | (C2×C43)⋊(C52×C7) |
| unambiguous semidirect product | (C2×C5×C43)⋊(C5×C7) |
| unambiguous semidirect product | (C2×C52×C43)⋊C7 |
| Fitting, socle, Hall | C2×C52×C43 ⋊ C7 |
| derived, Sylow | C43 ⋊ C2×C52×C7 |
| Hall | C52×C43 ⋊ C2×C7 |
| Hall | C2×C43 ⋊ C52×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52 | C43⋊C7 |
| commutator, cosocle, hypocenter | C43 | C2×C52×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C43 | C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2×C52 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2150 |
650 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×Dic43⋊C7, C5×(C43⋊C7)⋊Dic5, C5×Dic5×C43⋊C7, … |
| maximal normal subgroup of | C52×Dic43⋊C7, C5×(C43⋊C7)⋊Dic5, C5×Dic5×C43⋊C7, … |
| maximal quotient of | C4×C52×C43⋊C7, C22×C52×C43⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15050, 19);