Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C9 · Schur multiplier (H2) = C25 |
| direct product | C2×C9×#237 |
| Fitting | C2×C3×D4×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×#41 |
546 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13140397, #13140399, #13140405, … |
| maximal normal subgroup of | #13140397, #13140399, #13140405, … |
| maximal quotient of | C2×C9×#877, C2×C9×#878, C2×C9×#885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2578);