Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #92258 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C33 |
| direct product | C2×#11757562 |
| derived | C33 ⋊ C2×C32×C4 |
| Sylow | C32⋊H(3,𝔽3) ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #92258 |
| commutator, hypocenter | C33 | C2×C32×C4 |
| Frattini | C2×C32 | C2×C32×D3 |
| Fitting, prime radical | C22×C32⋊H(3,𝔽3) | C2 |
| socle | C22×C32 | C32×D3 |
| cosocle | C2×C33 | C22×C32 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C22 | |
753 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 753 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1817);