Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of (#4174⋊C2)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| Fitting | C2×#6909 ⋊ C22 |
| derived | AΣL(1,𝔽27) ⋊ C23×C3 |
| Sylow | #6909 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (#4174⋊C2)⋊C3 |
| commutator, cosocle, hypocenter | AΣL(1,𝔽27) | C23×C3 |
| Frattini | C32 | C2×C3×D32 |
| Fitting | C2×#6909 | C22 |
| socle | C2×C3 | C3×((C3⋊D3)⋊C3)⋊C2 |
| LCS | G ▷ AΣL(1,𝔽27) | |
| UCS | C1 ◁ C2 | |
458 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72212523, D3×(#4174⋊C2)⋊C3, C2×#72221953 |
| maximal quotient of | D3×(#4174⋊C2)⋊C3 |
| automorphism group of | #66322, #66330, C2×#4175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2700);