Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6258 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#88613 |
| derived | C22⋊H(3,𝔽3) ⋊ C2×C4 |
319 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 319 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | #13146398, #13146399, #13146401, … |
| maximal normal subgroup of | #13146398, #13146399, #13146401, … |
| maximal quotient of | C2×#11720736, #13147041, C4×#88613, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2364);