Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #88851 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C33 |
| direct product | C2×#88852 |
| Fitting | C2×C33×C8 ⋊ C2 |
| Sylow | C33 ⋊ C2×D8 |
1064 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
222 conjugacy classes — view the full character table.
| maximal subgroup of | #13145567, #13145568, #13145591, … |
| maximal normal subgroup of | #13145567, #13145568, #13145591, … |
| maximal quotient of | #13163322, C4×#88852, #13163334, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3911);