Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×#92392 |
| Fitting | C22×H(5,𝔽3) ⋊ C2 |
| Sylow | H(5,𝔽3) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | C32×C3⋊D3 |
| commutator, cosocle, hypocenter | H(3,𝔽3) | C23×C32 |
| Frattini | C3 | C22×C32×C3⋊D3 |
| Fitting | C22×H(5,𝔽3) | C2 |
| hypercenter | C22×H(3,𝔽3) | C3⋊D3 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C22×C3 ◁ C22×H(3,𝔽3) | |
1556 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1556 conjugacy classes of subgroups — too many to draw. Only its 251 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
232 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3763);