Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊D3×#1113 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
| direct product | C3⋊D3×#1113 |
| Fitting, socle, derived, Sylow | C35 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C35 | C23 |
| LCS | G ▷ C35 | |
| UCS | C1 | |
2028 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 2028 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | D33×C3⋊D3, D32×#1113, #72228610, … |
| maximal normal subgroup of | D33×C3⋊D3, D32×#1113, #72228610, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3939);