Finite Group DatabasebetaFinite Group Databasebeta| order | 512 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #63011 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C219 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C26 |
| commutator, Frattini, socle, cosocle | C22 | C27 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ G | |
| LECS | G ▷ C22 ▷ C1 | |
35126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
Polycyclic presentation:
2^9|g^2=h,b^a=bh,c^a=ci,d^a=dh,c^b=chi,f^e=fi152 conjugacy classes — view the full character table.
| maximal subgroup of | #72231699, #72233733, #72236881, … |
| maximal normal subgroup of | #72231699, #72233733, #72236881, … |
| maximal quotient of | #72234447, #72234464, #72236836, … |
| automorphism group of | #1378, #2117 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(512, 10493538);