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Cayley diagram

C2×#16683 #611346

order512
nilpotency class2
isoclinismisoclinic class of #16249
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#16683

Subgroups

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

4278 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 512

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 518542);