Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #92391 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C32 |
No aliases for this group.
| derived | C33 ⋊ C32×C8 |
| Sylow | H(5,𝔽3) ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #92391 |
| commutator, hypocenter | C33 | C32×C8 |
| Frattini | C3×C4 | C32×C3⋊D3 |
| Fitting | C4×H(5,𝔽3) | C2 |
| socle | C2×C3 | C32×C3⋊Dic3 |
| prime radical | C2×H(5,𝔽3) | C4 |
| cosocle | C33×C4 | C2×C32 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C4 | |
567 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 567 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2,3^2,2^2,3^3|a^2=d,d^2=e,f^a=f^2,g^a=g^2,h^a=h^2,g^b=gh,f^c=fh220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2269);