Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of D175 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic175 |
| derived, Hall | C7×C25 ⋊ C3×C4 |
| Hall | C3×C7×C25 ⋊ C4 |
| Hall | C3×C25 ⋊ Dic7 |
| Sylow | C25 ⋊ C3×Dic7 |
| Hall | C3×C7 ⋊ Dic25 |
| Sylow | C7 ⋊ C3×Dic25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D175 |
| commutator, hypocenter | C7×C25 | C3×C4 |
| Frattini | C2×C5 | C3×D35 |
| Fitting | C2×C3×C7×C25 | C2 |
| socle, prime radical | C2×C3×C5×C7 | D5 |
| cosocle | C2×C7×C25 | C2×C3 |
| LCS | G ▷ C7×C25 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2100 |
534 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 8);