Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6229 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#88527 |
| Fitting | C2×C8×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C2×M16 |
374 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 96 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 | #13135098, #13135861, #13136913, … |
| maximal normal subgroup of | #13135098, #13135861, #13136913, … |
| maximal quotient of | #13143764, #13143770, C4×#88527, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1742);