Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#88651 |
| Sylow | H(3,𝔽3) ⋊ C22×Q8 |
600 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 132 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 | #13138041, #13138042, #13138043, … |
| maximal normal subgroup of | #13138041, #13138042, #13138043, … |
| maximal quotient of | #13147751, #13147754, #13147767, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2452);