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Cayley diagram

C2×#15618 #609234

order512
nilpotency class2
isoclinismisoclinic class of #15257
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#15618

Subgroups

subgroupG/H
center, socle, prime radicalC25C24
commutator, Frattini, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

4138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 512

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 516430);