Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of D15⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D15⋊D5 |
| unambiguous semidirect product | D15⋊(C7×D5) |
| Fitting, socle, Hall | C3×C52×C7 ⋊ C22 |
| derived, Hall | C3×C52 ⋊ C22×C7 |
| Hall | C52×C7 ⋊ C2×D3 |
| Sylow | C52 ⋊ C2×D3×C7 |
| Hall | C3×C7 ⋊ D52 |
| Sylow | C3 ⋊ C7×D52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D15⋊D5 |
| commutator, cosocle, hypocenter | C3×C52 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C7 | C22 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C7 | |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 210 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,3,4,5,6,7)(8,9,10)(11,12)(13,14)(17,18)(19,20);(9,10)(12,13)(14,15)(16,17,19,20,18)210 conjugacy classes — view the full character table.
| maximal subgroup of | C49×D15⋊D5, C72×D15⋊D5, C7×#14523665, … |
| maximal normal subgroup of | C49×D15⋊D5, C72×D15⋊D5, C7×C11×D15⋊D5, … |
| maximal quotient of | C49×D15⋊D5, C72×D15⋊D5, C7×#14523665, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 144);