Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of D5×D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D5×D15 |
| unambiguous semidirect product | (C3×D5)⋊(C7×D5) |
| unambiguous semidirect product | (C5×D5)⋊(D3×C7) |
| 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 | D5×D15 |
| 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.
| transitive degree | μt(G) = 210 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D15×C49, C72×D5×D15, C7×D5×D105, … |
| maximal normal subgroup of | D5×D15×C49, C72×D5×D15, C7×D5×C11×D15, … |
| maximal quotient of | D5×D15×C49, C72×D5×D15, C7×D5×D105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 140);