Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #88368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#88370 |
| Sylow | C27 ⋊ C2×Q16 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #13134259, #13134299, #13134303, … |
| maximal normal subgroup of | #13134259, #13134299, #13134303, … |
| maximal quotient of | C2×#11720047, #13134470, C2×#11720049, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 157);