Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, derived, Sylow | C32×H(3,𝔽3) ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #10620197 |
| commutator, Fitting, hypocenter | C32×H(3,𝔽3) | C2×C4 |
| socle | C33 | C2×#157 |
| prime radical | C3⋊D3×#272 | C2 |
| cosocle | C32×#272 | C22 |
| LCS | G ▷ C32×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
407 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 407 conjugacy classes of subgroups — too many to draw. Only its 26 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|b^2=c,f^a=f^2,g^a=g^2,d^b=de^2h,e^b=d^2e^2h^2,f^b=f^2,d^c=d^2,e^c=e^2,e^d=eh66 conjugacy classes — view the full character table.
| maximal subgroup of | #72259730, #72259834, #72259932 |
| maximal normal subgroup of | #72259730, #72259834, #72259932 |
| maximal quotient of | #72228673 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3496);