Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C4⋊#4207 |
| Fitting | C2×C4×#737 ⋊ C2 |
| Sylow | #737 ⋊ C2×D4 |
477 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 477 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4×#4207 |
| maximal normal subgroup of | C2×D4×#4207 |
| maximal quotient of | C2×C4⋊#92299 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2622);