Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D9×C3⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×D9×C3⋊D9 |
| Fitting | C2×C3×C92 ⋊ C22 |
| derived, Sylow | C3×C92 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D9×C3⋊D9 |
| commutator, cosocle, hypocenter | C3×C92 | C23 |
| Frattini | C32 | C2×D3×C3⋊D3 |
| Fitting | C2×C3×C92 | C22 |
| socle | C2×C33 | D32 |
| LCS | G ▷ C3×C92 | |
| UCS | C1 ◁ C2 | |
720 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72214284, C2×D3×D92, #72259402, … |
| maximal normal subgroup of | C2×#72214284, C2×D3×D92, #72259402, … |
| maximal quotient of | #72259402, D3×D9×C3⋊D9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2703);