Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of D5×C5⋊AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D5×C5⋊AGL(1,𝔽7) |
| unambiguous semidirect product | (C5×D5)⋊AGL(1,𝔽7) |
| unambiguous semidirect product | (D5×ΓL(1,𝔽8))⋊D5 |
| unambiguous semidirect product | (D5×D35)⋊C3 |
| Fitting, socle, derived, Hall | C52×C7 ⋊ C22×C3 |
| Hall | D5×D35 ⋊ C3 |
| Hall | C52×ΓL(1,𝔽8) ⋊ C22 |
| Sylow | C52 ⋊ C2×AGL(1,𝔽7) |
| Hall | ΓL(1,𝔽8) ⋊ D52 |
| Sylow | C7 ⋊ C3×D52 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C7 | C22×C3 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 70 |
68 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 80);