Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C32⋊H(3,𝔽3) ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | ((C3⋊D3)⋊C3)⋊D3 |
| commutator, Fitting, cosocle | C2×C32⋊H(3,𝔽3) | C22 |
| Frattini, socle | C2×C32 | D3×C3⋊D3 |
| hypocenter | C32⋊H(3,𝔽3) | D4 |
| LCS | G ▷ C2×C32⋊H(3,𝔽3) ▷ C32⋊H(3,𝔽3) | |
| UCS | C1 ◁ C2×C3 | |
586 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
2^3,3^5|a^2=c,b^a=bc,f^a=f^2,h^a=h^2,d^b=d^2,e^b=e^2,h^b=h^2,e^d=eg,f^e=fh69 conjugacy classes — view the full character table.
| maximal subgroup of | #72219706, #72219728, #72219729, … |
| maximal normal subgroup of | #72219706, #72219728, #72219729, … |
| maximal quotient of | #72229250 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1382);