Finite Group DatabasebetaFinite Group Databasebeta| order | 512 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C211×C4 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C23 | C26 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
4584 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
Polycyclic presentation:
2^9|a^2=g,b^2=g,c^2=g,b^a=bg,c^a=ch,d^a=dh,e^a=ehi,f^a=fghi,d^b=di,e^b=eg,f^b=fh,d^c=dg,e^c=eh,f^c=fhi71 conjugacy classes — view the full character table.
| derived subgroup of | #72227469 |
| Fitting subgroup of | #72227469 |
| maximal subgroup of | #72227469 |
| maximal normal subgroup of | #72227469 |
| maximal quotient of | #72227965, #72228716 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(512, 10481185);