Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #634⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C2×#3743⋊C3 |
| unambiguous semidirect product | (C2×#3743)⋊C3 |
| Fitting | C2×C8×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C2×M16 |
260 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | #13135092, #10589380⋊C3, #13138768, … |
| maximal normal subgroup of | #13135092, #10589380⋊C3, #13138768, … |
| maximal quotient of | #10592378⋊C3, #10592384⋊C3, C4×#3743⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1468);