Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #14519546 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C35 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C35 | C23 |
| LCS | G ▷ C35 | |
| UCS | C1 | |
2796 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 2796 conjugacy classes of subgroups — too many to draw. Only its 113 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|d^a=d^2,e^a=e^2,h^a=h^2,d^b=d^2,e^b=e^2,f^b=f^2,f^c=f^2,g^c=g^287 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#10620215, #72226753, #72226754, … |
| maximal normal subgroup of | D3×#10620215, #72228531, #72228540, … |
| maximal quotient of | #72277838, #72277879 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3940);