Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of (C5⋊D5)⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×(C5⋊D5)⋊D7 |
| Fitting, socle, Hall | C3×C52×C7 ⋊ C22 |
| derived, Hall | C52×C7 ⋊ C22×C3 |
| Hall | C3×C52 ⋊ C2×D7 |
| Sylow | C52 ⋊ C2×C3×D7 |
| Hall | C3×C7 ⋊ D52 |
| Sylow | C7 ⋊ C3×D52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C5⋊D5)⋊D7 |
| commutator, cosocle, hypocenter | C52×C7 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C7 | C22 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 210 |
174 conjugacy classes — view the full character table.
| maximal subgroup of | C3×(C5⋊D5)⋊D49, #28413326, #28413328, … |
| maximal normal subgroup of | C3×C7×(C5⋊D5)⋊D7, C3×C11×(C5⋊D5)⋊D7, C3×C13×(C5⋊D5)⋊D7, … |
| maximal quotient of | C3×(C5⋊D5)⋊D49, #28413326, #28413328, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 120);