Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #3754⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#3753⋊C3 |
| unambiguous semidirect product | (C2×#3753)⋊C3 |
| Fitting | C2×D4×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C2×D8 |
320 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
82 conjugacy classes — view the full character table.
| maximal subgroup of | #13140525, #13140526, #13140527, … |
| maximal normal subgroup of | #13140525, #13140526, #13140527, … |
| maximal quotient of | C2×#63634⋊C3, C2×#63636⋊C3, #10592666⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1601);