Finite Group DatabasebetaFinite Group Databasebeta| order | 512 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10574873 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | C23×#120 |
| commutator, Frattini, cosocle | C23 | C26 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×#41 ◁ G | |
| LECS | G ▷ C23 ▷ C2 ▷ C1 | |
22163 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 32 |
Polycyclic presentation:
2^9|b^a=bg,c^a=ch,d^a=di,h^b=hi,g^c=gi,e^d=ei,f^d=fi,f^e=fi113 conjugacy classes — view the full character table.
| maximal subgroup of | #72215901, #72215925, #72215953, … |
| maximal normal subgroup of | #72215901, #72215925, #72215953, … |
| maximal quotient of | #72252417, #72252418, #72252423, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(512, 10482071);