Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of (C3⋊#1113)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×(C3⋊#1113)⋊C3 |
| unambiguous semidirect product | (C2×C3⋊#1113)⋊C3 |
| Fitting | C2×C32×H(3,𝔽3) ⋊ C22 |
| derived | C34 ⋊ C23×C3 |
| Sylow | C32×H(3,𝔽3) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (C3⋊#1113)⋊C3 |
| commutator, cosocle, hypocenter | C34 | C23×C3 |
| Frattini | C3 | C2×C3×#1113 |
| Fitting | C2×C32×H(3,𝔽3) | C22 |
| socle | C2×C33 | C2×C3×D3 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C2 | |
911 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 911 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D32×(C3⋊D3)⋊C3, C2×#72214370, C2×#14519181, … |
| maximal normal subgroup of | C2×D32×(C3⋊D3)⋊C3, C2×#14519181, #72260018 |
| maximal quotient of | #72260018 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3710);