Finite Group DatabasebetaFinite Group Databasebeta| order | 2268 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C32 |
| direct product | D7×C3⋊#272 |
| Fitting, derived, Hall | C3×C7×H(3,𝔽3) ⋊ C22 |
| Sylow | C3×H(3,𝔽3) ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×C3⋊#272 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D7×C3⋊(C3⋊D3) |
| commutator, Fitting, cosocle, hypocenter | C3×C7×H(3,𝔽3) | C22 |
| socle | C32×C7 | C2×C3⋊D3 |
| LCS | G ▷ C3×C7×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
480 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 126 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#92300, AGL(1,𝔽7)×C3⋊#272, #72269700 |
| maximal normal subgroup of | D7×#92300, AGL(1,𝔽7)×C3⋊#272, #72269700 |
| maximal quotient of | D7×#92338 |
Past the SmallGroups library coverage — no SmallGroups id.