Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C34 · Schur multiplier (H2) = C2×C35 |
| direct product | C2×C22⋊H(5,𝔽3) |
| unambiguous semidirect product | C23⋊H(5,𝔽3) |
| Fitting | C23×C3×H(3,𝔽3) ⋊ C3 |
| Sylow | C23 ⋊ H(5,𝔽3) |
1396 conjugacy classes of subgroups; only the 484 normal subgroups are shown.
This group has 1396 conjugacy classes of subgroups — too many to draw. Only its 484 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
232 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3737);