Finite Group DatabasebetaFinite Group Databasebeta| order | 10500 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | AGL(1,𝔽7)×#6953 |
| Fitting, derived, Hall | C7×H(3,𝔽5) ⋊ C22×C3 |
| Hall | D7×#6953 ⋊ C3 |
| Hall | ΓL(1,𝔽8)×H(3,𝔽5) ⋊ C22 |
| Sylow | H(3,𝔽5) ⋊ C2×AGL(1,𝔽7) |
| Hall | ΓL(1,𝔽8) ⋊ C2×#6953 |
| Sylow | C7 ⋊ C2×C3×#6953 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | AGL(1,𝔽7)×C5⋊D5 |
| commutator, Fitting, cosocle, hypocenter | C7×H(3,𝔽5) | C22×C3 |
| socle | C5×C7 | C2×C3×C5⋊D5 |
| LCS | G ▷ C7×H(3,𝔽5) | |
| UCS | C1 ◁ C5 | |
300 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
154 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×#92539 |
| maximal normal subgroup of | AGL(1,𝔽7)×#92539 |
Past the SmallGroups library coverage — no SmallGroups id.