Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of ((C3⋊D3)⋊C9)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×((C3⋊D3)⋊C9)⋊C2 |
| Fitting | C2×C3×C32⋊C9 ⋊ C22 |
| derived | C32⋊C9 ⋊ C23×C3 |
| Sylow | C3×C32⋊C9 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | ((C3⋊D3)⋊C9)⋊C2 |
| commutator, cosocle, hypocenter | C32⋊C9 | C23×C3 |
| Frattini | C32 | C2×C3×D32 |
| Fitting | C2×C3×C32⋊C9 | C22 |
| socle | C2×C33 | D32 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C2×C3 | |
553 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 553 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72221854, C2×#72221861 |
| maximal normal subgroup of | C2×#72221861 |
| maximal quotient of | C2×#72221850, C2×#72221852, C2×#72221853 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2675);