Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C9⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C34 · Schur multiplier (H2) = C2×C37 |
| direct product | C2×C32×C22⋊H(3,𝔽3) |
| Fitting | C23×C34 ⋊ C3 |
| Sylow | C23 ⋊ C32×H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C33 | C3×A4 |
| commutator, cosocle | C22×C3 | C2×C34 |
| Frattini | C3 | C2×C33×A4 |
| Fitting | C23×C34 | C3 |
| socle | C23×C33 | C32 |
| hypercenter | C2×C34 | A4 |
| hypocenter | C22 | C2×C32×H(3,𝔽3) |
| LCS | G ▷ C22×C3 ▷ C22 | |
| UCS | C1 ◁ C2×C33 ◁ C2×C34 | |
2648 conjugacy classes of subgroups; only the 568 normal subgroups are shown.
This group has 2648 conjugacy classes of subgroups — too many to draw. Only its 568 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3745);