Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C9⋊(C22⋊A4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C24 |
| direct product | C2×#88907 |
| Sylow | C25 ⋊ 3−1+2 |
832 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #13141227, C2×#11721347, #13164538, … |
| maximal normal subgroup of | #13141227, C2×#11721347, #13164538, … |
| maximal quotient of | C4×#88907, C2×#11722586, #13164883, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4042);