Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #88587 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#88587 |
| Sylow | H(3,𝔽3) ⋊ C2×SD16 |
194 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
46 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#88587, #13146570, #13146571, … |
| maximal normal subgroup of | C4×#88587, #13146570, #13146571, … |
| maximal quotient of | #13146507, #13146510, #13146513, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2273);