Finite Group DatabasebetaFinite Group Databasebeta| order | 2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×ΓL(1,𝔽8)⋊#261 |
| Fitting, socle | C2×C7×C13 ⋊ C3×C4 |
| derived, Hall | C7×C13 ⋊ C2×C3×C4 |
| Hall | C2×C7⋊#261 ⋊ C3 |
| Hall | C13×ΓL(1,𝔽8) ⋊ C2×C4 |
| Hall | ΓL(1,𝔽8) ⋊ C2×#261 |
| Sylow | C13 ⋊ C2×ΓL(1,𝔽8)⋊C4 |
| Sylow | C7 ⋊ C2×C3×#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | ΓL(1,𝔽8)⋊#261 |
| commutator, hypocenter | C7×C13 | C2×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C13 | C3×C4 |
| prime radical | C2×ΓL(1,𝔽8)×D13 | C2 |
| cosocle | C7×D13 | C22×C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C2 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 182 |
58 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽7)×#261, C2×ΓL(1,𝔽8)⋊AGL(1,𝔽13) |
| maximal normal subgroup of | C2×AGL(1,𝔽7)×#261, C2×ΓL(1,𝔽8)⋊AGL(1,𝔽13) |
Past the SmallGroups library coverage — no SmallGroups id.