Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #88627 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#88631 |
| Sylow | H(3,𝔽3) ⋊ C2×M16 |
210 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | #13136720, #13136721, #13136736, … |
| maximal normal subgroup of | #13136720, #13136721, #13136736, … |
| maximal quotient of | C2×#11720783, C4×#88631, C2×#11720785, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2421);