Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #41×#272 |
| Fitting | #41×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C2×#41 |
902 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 902 conjugacy classes of subgroups — too many to draw. Only its 172 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #13141072, #13141073, #104×#272, … |
| maximal normal subgroup of | #13141072, #13141073, #104×#272, … |
| maximal quotient of | #13153886, #13153887, #13153888, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2641);