Finite Group DatabasebetaFinite Group Databasebeta| order | 1050 |
| isoclinism | isoclinic class of C7⋊#3874 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#3874 |
| Fitting, socle, Hall | C52×C7 ⋊ D3 |
| derived, Hall | C7×C52⋊C3 ⋊ C2 |
| Hall | C52⋊C3 ⋊ D7 |
| Sylow | C52 ⋊ D21 |
| Sylow | C7 ⋊ #3874 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C7×C52⋊C3 | C2 |
| Fitting, socle | C52×C7 | D3 |
| LCS | G ▷ C7×C52⋊C3 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 105 |
Polycyclic presentation:
2,3,7,5^2|b^a=b^2,c^a=c^6,d^a=d^2e,e^a=d^2e^3,d^b=d^2e^4,e^b=d^2e^246 conjugacy classes — view the full character table.
| maximal subgroup of | #3874⋊D7, ((C5⋊D5)⋊C3)⋊D7, D7×#3874, … |
| maximal normal subgroup of | #3874⋊D7, ((C5⋊D5)⋊C3)⋊D7, D7×#3874, … |
| maximal quotient of | C7⋊#64470, C2×C7⋊#3874, C7⋊#90646, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1050, 14);