Finite Group Databasebeta

← Prev (#10585962) Next (#10585964) →

Cayley diagram

C22×#3516 #10585963

order512
nilpotency class2
isoclinismisoclinic class of #3484
automorphism?
homologyAbelianization (H1) = C27 · Schur multiplier (H2) = C219

Aliases

direct productC22×#3516

Subgroups

subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC22C27
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C22 ▷ C1

34690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 256

A minimal faithful permutation representation — 7 generators on 28 points:

(1,2);(3,4);(6,9)(10,12)(14,17)(15,21)(20,24)(22,27);(13,14,18,17)(15,19,21,23)(16,24,25,20)(22,28,27,26);(5,6)(7,10)(8,9)(11,12)(13,15)(14,19)(16,22)(17,23)(18,21)(20,26)(24,28)(25,27);(13,16,18,25)(14,20,17,24)(15,22,21,27)(19,26,23,28);(5,7,8,11)(6,10,9,12)(13,17,18,14)(15,23,21,19)(16,24,25,20)(22,28,27,26)

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493159);