Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | D8×(C3⋊D3)⋊C3 |
| unambiguous semidirect product | (D8×C3⋊D3)⋊C3 |
| Fitting | D8×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C2×D8 |
288 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | #13139245, #13139247, #13139249, … |
| maximal normal subgroup of | #13139245, #13139247, #13139249, … |
| maximal quotient of | #10592458⋊C3, #10592485⋊C3, #10592459⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1502);