Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6308 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C33 |
| direct product | C2×C4⋊(C3⋊(C3⋊Dic3)) |
| Sylow | C33 ⋊ C2×C4⋊C4 |
1288 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | #13145652, #13145653, #13145659, … |
| maximal normal subgroup of | #13145652, #13145653, #13145659, … |
| maximal quotient of | C2×C4⋊(C3⋊(C3⋊(C3⋊C8))), #13163564, C4×C4⋊(C3⋊(C3⋊Dic3)), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3933);