Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×D27 |
| Fitting | C2×Q8×C27 ⋊ C2 |
| Sylow | C27 ⋊ C22×Q8 |
312 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | #101×D27, #103×D27, #13134308, … |
| maximal normal subgroup of | #101×D27, #103×D27, #13134308, … |
| maximal quotient of | C2×#11720136, C2×#11720145, C2×#11720137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 638);