Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C3⋊PSU(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#88945 |
| Sylow | C33 ⋊ C2×C4⋊C4 |
226 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | #13165795, #13165797, #13165799, … |
| maximal normal subgroup of | #13165795, #13165797, #13165799, … |
| maximal quotient of | #13167661, C2×#11722803, #13167664, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4333);