Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #88528 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#88528 |
| Fitting | C2×C8×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C2×SD16 |
374 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
106 conjugacy classes — view the full character table.
| maximal subgroup of | #13138957, #13138959, #13138966, … |
| maximal normal subgroup of | #13138957, #13138959, #13138966, … |
| maximal quotient of | #13143765, #13143766, C4×#88528, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1744);