Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #272 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×C8×#272 |
| Fitting | C2×C8×H(3,𝔽3) ⋊ C2 |
| derived, Sylow | H(3,𝔽3) ⋊ C22×C8 |
418 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #13135097, #13135845, #13136910, … |
| maximal normal subgroup of | #13135097, #13135845, #13136910, … |
| maximal quotient of | C8×#6229, C4×C8×#272, #13143770, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1741);