Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of D21×C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
| direct product | D21×C5⋊D5 |
| Fitting, socle, derived, Hall | C3×C52×C7 ⋊ C22 |
| Hall | C52×C7 ⋊ C2×D3 |
| Hall | C3×C52 ⋊ C2×D7 |
| Sylow | C52 ⋊ C2×D21 |
| Hall | C3×C7 ⋊ C2×C5⋊D5 |
| Sylow | C7 ⋊ D3×C5⋊D5 |
| Sylow | C3 ⋊ D7×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C7 | C22 |
| LCS | G ▷ C3×C52×C7 | |
| UCS | C1 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 525 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C5⋊D5×D147, C7×D21×C5⋊D5, C5⋊D5×C3⋊(C7⋊D7), … |
| maximal normal subgroup of | C7×D21×C5⋊D5, C11×D21×C5⋊D5, C13×D21×C5⋊D5, … |
| maximal quotient of | C5⋊D5×D147, C7×D21×C5⋊D5, C5⋊D5×C3⋊(C7⋊D7), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 137);