Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C27 · Schur multiplier (H2) = C22 |
| direct product | D4×C22⋊C27 |
| unambiguous semidirect product | C4⋊(C2×C22⋊C27) |
| unambiguous semidirect product | (C22×D4)⋊C27 |
| Sylow | C22×D4 ⋊ C27 |
166 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | #13136152, #13136153, D8×C22⋊C27, … |
| maximal normal subgroup of | #13136152, #13136153, D8×C22⋊C27, … |
| maximal quotient of | C22⋊C4×C22⋊C27, C4⋊C4×C22⋊C27, #548⋊C27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 623);