Finite Group DatabasebetaFinite Group Databasebeta| order | 4200 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#63306⋊C3 |
| Hall | C5×#63306 ⋊ C3 |
| Hall | C52×ΓL(1,𝔽8) ⋊ D4 |
| Hall | C52×C7 ⋊ C3×D4 |
| Sylow | C52 ⋊ C4⋊AGL(1,𝔽7) |
| Hall | ΓL(1,𝔽8) ⋊ C5×C22⋊D5 |
| Sylow | C7 ⋊ C3×C5×C22⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D5×AGL(1,𝔽7) |
| commutator, cosocle | C2×C5×C7 | C22×C3×C5 |
| Frattini | C2 | C5×D5×AGL(1,𝔽7) |
| Fitting, socle | C2×C52×C7 | C22×C3 |
| hypocenter | C5×C7 | C3×C5×D4 |
| LCS | G ▷ C2×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C2×C5 | |
168 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 140 |
235 conjugacy classes — view the full character table.
| maximal subgroup of | #72243182, C5×C22⋊D5×AGL(1,𝔽7), #72243213 |
| maximal normal subgroup of | #72243182, C5×C22⋊D5×AGL(1,𝔽7), #72243213 |
Past the SmallGroups library coverage — no SmallGroups id.