Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6196 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#6196 |
| Sylow | H(3,𝔽3) ⋊ C22×Q8 |
600 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | #13140223, #13140224, #13140225, … |
| maximal normal subgroup of | #13140223, #13140224, #13140225, … |
| maximal quotient of | C2×#11721093, C2×#11721095, C2×C4×#6196, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2503);