Finite Group DatabasebetaFinite Group Databasebeta| order | 512 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C219 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C22 | C27 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ G | |
| LECS | G ▷ C22 ▷ C1 | |
Only the 29228 normal subgroups are shown; non-normal subgroups are omitted.
Polycyclic presentation:
2^9|d^2=i,g^2=h,b^a=bh,c^a=ci,d^a=dh,g^a=gi,c^b=ch,d^b=di,f^e=fi140 conjugacy classes — view the full character table.
| maximal subgroup of | #72236765, #72315163 |
| maximal normal subgroup of | #72236765, #72315163 |
| maximal quotient of | #72238159, #72238246, #72312837, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(512, 10493823);