Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #92333 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C4×#92333 |
| Fitting | C4×#6911 ⋊ C2 |
| derived | #732 ⋊ C2×C3×C4 |
| Sylow | #6911 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #92333 |
| commutator, hypocenter | #732 | C2×C3×C4 |
| Frattini | C2×C32 | C2×C3×C3⋊D3 |
| Fitting | C4×#6911 | C2 |
| socle | C2×C3 | C2×C3×#272 |
| prime radical | C2×#92333 | C2 |
| cosocle | C2×#732 | C22×C3 |
| LCS | G ▷ #732 | |
| UCS | C1 ◁ C4 | |
406 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#13091120, D4×#92333, C4×(#4178⋊C2)⋊C3, … |
| maximal normal subgroup of | D4×#92333, C4×(#4178⋊C2)⋊C3, #72259376 |
| maximal quotient of | AGL(1,𝔽5)×#92333 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2014);