Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of (((C3⋊D3)⋊C3)⋊C2)⋊(C3⋊D3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | (((C3⋊D3)⋊C3)⋊C2)⋊(C3⋊D3) |
| Fitting, Sylow | C32×H(3,𝔽3) ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle | C32×#272 | C22 |
| Frattini | C3 | D32⋊(C3⋊D3) |
| Fitting, hypocenter | C32×H(3,𝔽3) | D4 |
| socle | C33 | GO+(4,𝔽2) |
| LCS | G ▷ C32×#272 ▷ C32×H(3,𝔽3) | |
| UCS | C1 | |
522 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2^3,3^5|b^a=bc,d^a=e,e^a=d,f^a=f^2,g^a=g^2,h^a=h^2,d^b=d^2,h^b=h^2,d^c=d^2,e^c=e^2,e^d=eh57 conjugacy classes — view the full character table.
| maximal subgroup of | #72259765, D3×(((C3⋊D3)⋊C3)⋊C2)⋊D3 |
| maximal normal subgroup of | #72259765, D3×(((C3⋊D3)⋊C3)⋊C2)⋊D3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3518);