Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | #67×#272 |
| Fitting | C22×C3×H(3,𝔽3) ⋊ C22 |
| Sylow | C3×H(3,𝔽3) ⋊ C2×D4 |
770 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | #72219728, #72219731, #67×C3⋊#272, … |
| maximal normal subgroup of | #72219731, D3×D4×#272 |
| maximal quotient of | #67×C3⋊#272, #72259736, #72259905 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2452);