Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of (C22⋊C27)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×(C22⋊C27)⋊C2 |
| derived | C22⋊C27 ⋊ C2×C4 |
136 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | C8×(C22⋊C27)⋊C2, #13136138, C2×C4×(C22⋊C27)⋊C2, … |
| maximal normal subgroup of | C8×(C22⋊C27)⋊C2, #13136138, C2×C4×(C22⋊C27)⋊C2, … |
| maximal quotient of | C4×#88390, #13136126, C4×#88391, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 612);