Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of D52×ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D52×ΓL(1,𝔽8) |
| unambiguous semidirect product | (C5×D5)⋊(C2×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C7×D52)⋊C3 |
| Fitting, socle, derived, Hall | C52×C7 ⋊ C22×C3 |
| Hall | C7×D52 ⋊ C3 |
| Hall | C52×ΓL(1,𝔽8) ⋊ C22 |
| Sylow | C52 ⋊ C22×ΓL(1,𝔽8) |
| 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 |
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 82);