Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #88627 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊#1088 |
| Fitting | C2×C4×H(3,𝔽3) ⋊ C4 |
| Sylow | H(3,𝔽3) ⋊ C2×C4⋊C4 |
246 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | #13136699, #13136700, #13136733, … |
| maximal normal subgroup of | #13136699, #13136700, #13136733, … |
| maximal quotient of | #13147311, #13147312, #13147313, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2414);