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Cayley diagram

C22×#2792 #7633565

order512
nilpotency class2
isoclinismisoclinic class of #2668
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C212

Aliases

direct productC22×#2792

Subgroups

subgroupG/H
center, socle, prime radicalC25C24
commutator, Frattini, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C23 ▷ C1

6930 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 512

A minimal faithful permutation representation — 6 generators on 28 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7540761);