Finite Group DatabasebetaFinite Group Databasebeta| order | 512 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C212 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, prime radical, cosocle | C23 | C26 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
3428 conjugacy classes of subgroups.
| transitive degree | μt(G) = 512 |
Polycyclic presentation:
2^9|a^2=gi,b^2=gh,c^2=h,d^2=g,e^2=ghi,f^2=gi,b^a=bg,c^a=ch,d^a=dh,e^a=ei,f^a=fg,c^b=ci,d^b=dhi,e^b=eg,f^b=fh,d^c=dgi,e^c=eh,f^c=fi,e^d=ei71 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(512, 10481182);