Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6229 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×C4⋊#272 |
| Fitting | C22×C4×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C22×D4 |
1298 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11720324, #13140013, C2×#11720325, … |
| maximal normal subgroup of | C2×#11720324, #13140013, C2×#11720325, … |
| maximal quotient of | C2×#11721715, C2×C4×C4⋊#272, C2×#11721720, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2624);