Finite Group Databasebeta

← Prev (#608279) Next (#608281) →

Cayley diagram

C2×#15111 #608280

order512
nilpotency class2
isoclinismisoclinic class of #14715
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#15111

Subgroups

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

3510 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 512

A minimal faithful permutation representation — 5 generators on 30 points:

(1,2);(3,4,5,6)(8,11)(12,14)(15,16,18,20)(17,19,21,22)(24,27)(28,30);(3,4)(5,6)(17,21)(19,22)(23,24,26,27)(25,28,29,30);(7,8,10,11)(9,12,13,14)(15,17,18,21)(16,19,20,22)(23,24)(25,28)(26,27)(29,30);(7,9,10,13)(8,12,11,14)(15,16)(17,19)(18,20)(21,22)(23,25,26,29)(24,28,27,30)

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, 515476);