Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of D21⋊D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D21⋊D25 |
| unambiguous semidirect product | D75⋊D7 |
| unambiguous semidirect product | D175⋊D3 |
| Fitting, derived, Hall | C3×C7×C25 ⋊ C22 |
| Hall | C7×C25 ⋊ C2×D3 |
| Hall | C3×C25 ⋊ C2×D7 |
| Sylow | C25 ⋊ D3×D7 |
| Hall | C3×C7 ⋊ C2×D25 |
| Sylow | C7 ⋊ D3×D25 |
| Sylow | C3 ⋊ D7×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C7×C25 | C22 |
| Frattini | C5 | D15⋊D7 |
| socle | C3×C5×C7 | C2×D5 |
| LCS | G ▷ C3×C7×C25 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 525 |
Polycyclic presentation:
2^2,3,5,7,5|d^5=f^4,c^a=c^2,e^a=e^6,c^b=c^2,d^b=d^4f,f^b=f^4159 conjugacy classes — view the full character table.
| maximal subgroup of | D75⋊D49, C7×D21⋊D25, D75⋊(C7⋊D7), … |
| maximal normal subgroup of | C7×D21⋊D25, C11×D21⋊D25, C13×D21⋊D25, … |
| maximal quotient of | D75⋊D49, C7×D21⋊D25, D75⋊(C7⋊D7), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 30);