Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #634⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C4×#638⋊C3 |
| unambiguous semidirect product | (C4×#638)⋊C3 |
| Fitting | C22×C4×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C4×D4 |
383 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 383 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | #13140026, #13140027, #13140028, … |
| maximal normal subgroup of | #13140026, #13140027, #13140028, … |
| maximal quotient of | C4×#3750⋊C3, #10592632⋊C3, C4×#3752⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1566);