Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #272 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#88386 |
| derived, Sylow | H(3,𝔽3) ⋊ C2×C16 |
154 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #13135078, #13135079, #13135080, … |
| maximal normal subgroup of | #13135078, #13135079, #13135080, … |
| maximal quotient of | C4×#88386, C4⋊#88386, C2×#11720102, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 511);