Finite Group DatabasebetaFinite Group Databasebeta| order | 2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×#10587716⋊C2 |
| Fitting, socle | C2×C7×C13 ⋊ C22×C3 |
| derived, Hall | C7×C13 ⋊ C23×C3 |
| Hall | C2×D7×D13 ⋊ C3 |
| Hall | #63270 ⋊ C23 |
| Sylow | C13 ⋊ C22×AGL(1,𝔽7) |
| Sylow | C7 ⋊ C22×D13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10587716⋊C2 |
| commutator, cosocle, hypocenter | C7×C13 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C13 | C22×C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C2 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 182 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72222389, C2×AGL(1,𝔽7)×D13⋊C3 |
| maximal normal subgroup of | C2×#72222389, C2×AGL(1,𝔽7)×D13⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.