Finite Group DatabasebetaFinite Group Databasebeta| order | 512 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #1082705 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C24 | C25 |
| prime radical | C2×#2673 | C2 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
3573 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 256 |
A minimal faithful permutation representation — 5 generators on 28 points:
(2,3)(6,8)(13,14,18,19)(15,20,21,16)(17,22,25,26)(23,27,28,24);(10,12)(14,19)(15,21)(17,25)(24,27);(1,2,4,3)(9,10)(11,12)(13,15)(14,20)(16,19)(17,23)(18,21)(22,27)(24,26)(25,28);(1,2,4,3)(5,6)(7,8)(13,16,18,20)(14,21,19,15)(17,24,25,27)(22,28,26,23);(1,3,4,2)(13,17)(14,22)(15,23)(16,24)(18,25)(19,26)(20,27)(21,28)Polycyclic presentation:
2^9|a^2=f,c^2=g,d^2=fg,e^2=g,b^a=bf,c^a=cg,d^a=di,e^a=eg,c^b=ch,e^b=ef,d^c=df86 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(512, 990794);