Finite Group DatabasebetaFinite Group Databasebeta| order | 4368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#72222390 |
| Fitting, socle | C2×C7×C13 ⋊ C2×C3×C4 |
| derived, Hall | C7×C13 ⋊ C22×C3×C4 |
| Hall | C2×D7×#261 ⋊ C3 |
| Hall | #63271 ⋊ C22×C4 |
| Sylow | C13 ⋊ C2×C4×AGL(1,𝔽7) |
| Sylow | C7 ⋊ C22×AGL(1,𝔽13) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72222390 |
| commutator, hypocenter | C7×C13 | C22×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C13 | C2×C3×C4 |
| prime radical | C2×#10587717⋊C2 | C2 |
| cosocle | C7×D13 | C23×C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C2 | |
216 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 182 |
66 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽7)×AGL(1,𝔽13) |
| maximal normal subgroup of | C2×AGL(1,𝔽7)×AGL(1,𝔽13) |
Past the SmallGroups library coverage — no SmallGroups id.