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Cayley diagram

C22×#2845 #7633393

order512
nilpotency class2
isoclinismisoclinic class of #2812
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C212

Aliases

direct productC22×#2845

Subgroups

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

5914 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);(5,6,8,10)(7,9,11,12)(13,14,17,16)(15,18,19,20)(22,25)(26,27);(7,11)(9,12)(14,16)(18,20)(21,22,24,25)(23,26,28,27);(5,6)(7,9)(8,10)(11,12)(13,15,17,19)(14,18,16,20)(21,22)(23,27)(24,25)(26,28);(5,7)(6,9)(8,11)(10,12)(13,16,17,14)(15,18,19,20)(21,23,24,28)(22,26,25,27)

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, 7540589);