Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting, derived, Sylow | C32×H(3,𝔽3) ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #10620198 |
| commutator, Fitting, hypocenter | C32×H(3,𝔽3) | C2×C4 |
| socle | C33 | C2×#157 |
| prime radical | C3⋊D3×#272 | C2 |
| cosocle | C3⋊(C3⋊#272) | C22 |
| LCS | G ▷ C32×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
382 conjugacy classes of subgroups; only the 16 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 16 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,d^a=de,e^a=de^2,f^a=fg,g^a=fg^2h^2,d^b=d^2,e^b=e^2,d^c=d^2,e^c=e^2,f^c=f^2,g^c=g^2h,g^f=gh48 conjugacy classes — view the full character table.
| maximal subgroup of | #72228685, #72259730, #72259737 |
| maximal normal subgroup of | #72228685, #72259730, #72259737 |
| maximal quotient of | #72228655 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3497);