Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #14519511 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C32 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C35 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C35 | C2×C4 |
| prime radical | C3×C3⋊D32 | C2 |
| cosocle | C3×C3⋊(C3⋊(C3⋊D3)) | C22 |
| LCS | G ▷ C35 | |
| UCS | C1 | |
784 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
Polycyclic presentation:
2^3,3^5|a^2=c,d^a=de,e^a=de^2,f^a=fg,g^a=fg^2,h^a=h^2,d^b=d^2,e^b=e^2,d^c=d^2,e^c=e^2,f^c=f^2,g^c=g^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#10620198, #72214678, #72224552, … |
| maximal normal subgroup of | D3×#10620198, #72214678, #72224552, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3905);