Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of ΓL(1,𝔽8)×D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×ΓL(1,𝔽8)×D25 |
| unambiguous semidirect product | C25⋊(C22×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C2×C25)⋊(C2×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C2×C7×D25)⋊C3 |
| Fitting | C2×C7×C25 ⋊ C2×C3 |
| derived, Hall | C7×C25 ⋊ C22×C3 |
| Hall | C2×C7×D25 ⋊ C3 |
| Hall | ΓL(1,𝔽8)×C25 ⋊ C22 |
| Sylow | C25 ⋊ C22×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C2×C3×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | ΓL(1,𝔽8)×D25 |
| commutator, cosocle, hypocenter | C7×C25 | C22×C3 |
| Frattini | C5 | C2×D5×ΓL(1,𝔽8) |
| Fitting | C2×C7×C25 | C2×C3 |
| socle | C2×C5×C7 | C3×D5 |
| LCS | G ▷ C7×C25 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 350 |
140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 18);