Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6258 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#6258 |
| Fitting | C22×C32×C4 ⋊ D3 |
| derived | C22⋊H(3,𝔽3) ⋊ C2×C4 |
279 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 279 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | #6258⋊C8, #13146285, C8×#6258, … |
| maximal normal subgroup of | #6258⋊C8, #13146285, C8×#6258, … |
| maximal quotient of | C4×#88610, #13147002, C4×#88611, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2348);