Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6196 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×#6200 |
| Sylow | H(3,𝔽3) ⋊ C4×D4 |
383 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 383 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#6200, #13138921, #13138922, … |
| maximal normal subgroup of | C8×#6200, #13138921, #13138922, … |
| maximal quotient of | C4×#88436, #13137415, C4×#88437, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1120);