Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#1088 |
| Fitting | C2×C4×H(3,𝔽3) ⋊ C4 |
| derived, Sylow | H(3,𝔽3) ⋊ C2×C42 |
270 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #13136697, #13136698, #13136730, … |
| maximal normal subgroup of | #13136697, #13136698, #13136730, … |
| maximal quotient of | C4×#88626, #13147309, C4×#88627, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2413);