Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#88672 |
| Sylow | H(3,𝔽3) ⋊ C2×#41 |
628 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | #13137469, #13146678, #13146680, … |
| maximal normal subgroup of | #13137469, #13146678, #13146680, … |
| maximal quotient of | C2×#11721085, #13150611, C2×#11721098, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2506);