Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of D5×AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| Fitting, socle, Hall | C52×C7 ⋊ C22×C3 |
| derived | C5×C7 ⋊ C22×C3×C5 |
| Hall | C5×D5×D7 ⋊ 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 | C5 | D5×AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C5×C7 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7 | C22×C3 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C5 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 70 |
140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 72);