Finite Group DatabasebetaFinite Group Databasebeta| order | 512 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10574840 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C24×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×#41 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
21930 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
Polycyclic presentation:
2^9|g^2=i,b^a=bg,c^a=ch,f^a=fi,g^a=gi,d^b=di,e^b=ei,g^b=gi,e^d=ei116 conjugacy classes — view the full character table.
| maximal subgroup of | #72313276 |
| maximal normal subgroup of | #72313276 |
| maximal quotient of | #72313338, #72313385, #72313404, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(512, 10482040);