Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #272 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C16×#272 |
| Fitting | C16×H(3,𝔽3) ⋊ C2 |
| derived, Sylow | H(3,𝔽3) ⋊ C2×C16 |
154 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #13134914, #13134915, C32×#272, … |
| maximal normal subgroup of | #13134914, #13134915, C32×#272, … |
| maximal quotient of | C32×#272, #13135726, C16×#1084, … |
| automorphism group of | C17×3−1+2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 477);