Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #1088⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×(((C3⋊D3)⋊C3)⋊C2)⋊C4 |
| Sylow | H(3,𝔽3) ⋊ C2×C22⋊C4 |
386 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
52 conjugacy classes — view the full character table.
| maximal subgroup of | C4×(((C3⋊D3)⋊C3)⋊C2)⋊C4, #13146620, #13146621, … |
| maximal normal subgroup of | C4×(((C3⋊D3)⋊C3)⋊C2)⋊C4, #13146620, #13146621, … |
| maximal quotient of | C2×#11720694, #13146494, #13146495, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2280);