Finite Group DatabasebetaFinite Group Databasebeta| order | 2268 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C34 |
| direct product | C2×H(3,𝔽3)×AGL(1,𝔽7) |
| Fitting | C2×C7×H(3,𝔽3) ⋊ C2×C3 |
| Hall | ΓL(1,𝔽8)×H(3,𝔽3) ⋊ C22 |
| Hall | C2×D7 ⋊ C3×H(3,𝔽3) |
| Sylow | C7 ⋊ C22×C3×H(3,𝔽3) |
560 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 126 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | #72230258, C2×AGL(1,𝔽7)×(C3⋊D3)⋊C3, C2×#72224660, … |
| maximal normal subgroup of | C2×AGL(1,𝔽7)×(C3⋊D3)⋊C3, C2×AGL(1,𝔽7)×#272 |
| maximal quotient of | #72230258, C2×#72224660 |
Past the SmallGroups library coverage — no SmallGroups id.