Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×#272 |
| Fitting | C2×Q8×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C22×Q8 |
858 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 858 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #13140935, #13140938, #13140941, … |
| maximal normal subgroup of | #13140935, #13140938, #13140941, … |
| maximal quotient of | C2×#11721755, C2×#11721764, C2×#11721756, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2635);