Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of #14268461 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, Hall | C32×C52 ⋊ D4 |
| Sylow | C52 ⋊ #626 |
| Sylow | C32 ⋊ D52⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | C32×C5⋊D5 | C22 |
| Fitting, socle, hypocenter | C32×C52 | D4 |
| LCS | G ▷ C32×C5⋊D5 ▷ C32×C52 | |
| UCS | C1 | |
140 conjugacy classes of subgroups; only the 18 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 18 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 30 |
Polycyclic presentation:
2^3,3^2,5^2|b^2=c,b^a=bc,e^a=e^2,f^a=g,g^a=f,d^b=d^2,f^b=f^2,g^b=g^3,f^c=f^4,g^c=g^454 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 655);