Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #272 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×C4×#272 |
| Fitting | C32×C4×H(3,𝔽3) ⋊ C2 |
| derived | H(3,𝔽3) ⋊ C2×C32×C4 |
| Sylow | C32×H(3,𝔽3) ⋊ C2×C4 |
1624 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 1624 conjugacy classes of subgroups — too many to draw. Only its 204 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 324 |
360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3312);