Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of C5⋊(C5⋊AGL(1,𝔽7)) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C5⋊(C5⋊AGL(1,𝔽7)) |
| unambiguous semidirect product | (C2×C5)⋊(C5⋊AGL(1,𝔽7)) |
| unambiguous semidirect product | (C2×ΓL(1,𝔽8))⋊(C5⋊D5) |
| Fitting, socle | C2×C52×C7 ⋊ C2×C3 |
| derived, Hall | C52×C7 ⋊ C22×C3 |
| Hall | C2×C5⋊D35 ⋊ C3 |
| Hall | C52×ΓL(1,𝔽8) ⋊ C22 |
| Sylow | C52 ⋊ C2×AGL(1,𝔽7) |
| Hall | ΓL(1,𝔽8) ⋊ C2×C5⋊D5 |
| Sylow | C7 ⋊ C2×C3×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C5⋊(C5⋊AGL(1,𝔽7)) |
| commutator, cosocle, hypocenter | C52×C7 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C7 | C2×C3 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C2 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 350 |
134 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 98);