Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C22×C34 ⋊ D3 |
| derived | #11757866 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C32 | C3⋊(C3⋊S4) |
| commutator, cosocle, hypocenter | #11757866 | C2 |
| Fitting | C22×C34 | D3 |
| socle | C22×C32 | C3⋊(C3⋊D3) |
| LCS | G ▷ #11757866 | |
| UCS | C1 ◁ C32 | |
730 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 53 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:
2,3^5,2^2|b^a=b^2,c^a=c^2,d^a=d^2,g^a=gh,c^b=cf,d^b=de,g^b=h,h^b=gh93 conjugacy classes — view the full character table.
| maximal quotient of | #72259917 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2520);