Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of AGL(1,𝔽7)×D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, derived, Hall | C7×C25 ⋊ C22×C3 |
| Hall | D7×D25 ⋊ C3 |
| Hall | ΓL(1,𝔽8)×C25 ⋊ C22 |
| Sylow | C25 ⋊ C2×AGL(1,𝔽7) |
| Hall | ΓL(1,𝔽8) ⋊ C2×D25 |
| Sylow | C7 ⋊ C2×C3×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C7×C25 | C22×C3 |
| Frattini | C5 | D5×AGL(1,𝔽7) |
| socle | C5×C7 | C2×C3×D5 |
| LCS | G ▷ C7×C25 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 175 |
98 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 16);