Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C33 |
| direct product | C2×#11758052 |
| Fitting | C2×H(5,𝔽3) ⋊ C4 |
| derived, Sylow | H(5,𝔽3) ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C2×C3 | #66472 |
| commutator, hypocenter | H(5,𝔽3) | C2×C4 |
| Frattini | C3 | C2×#66472 |
| Fitting | C2×H(5,𝔽3) | C4 |
| prime radical | C2×#92404 | C2 |
| cosocle | #92404 | C22 |
| LCS | G ▷ H(5,𝔽3) | |
| UCS | C1 ◁ C2×C3 | |
826 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14519166, C2×#14519140, C2×#14519082, … |
| maximal normal subgroup of | C2×#14519166, C2×#14519140, C2×#14519082, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3688);