Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #88860 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C33 |
| direct product | C2×#88862 |
| Fitting | C2×C33×Q8 ⋊ C2 |
| Sylow | C33 ⋊ C2×SD16 |
952 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #13161148, #13161149, #13161152, … |
| maximal normal subgroup of | #13161148, #13161149, #13161152, … |
| maximal quotient of | C2×#11722178, C2×#11722179, #13163627, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3949);