Finite Group Databasebeta

← Prev (#6348694) Next (#6348696) →

Cayley diagram

C2×#18779 #6348695

order512
nilpotency class3
isoclinismisoclinic class of #18746
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#18779

Subgroups

subgroupG/H
center, socleC23C2×#120
commutator, Frattini, cosocleC42C25
prime radicalC24#120
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

2868 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 256

A minimal faithful permutation representation — 5 generators on 34 points:

(1,2);(3,4,7,10)(5,11,13,18)(6,14,16,9)(8,15,17,12)(19,20,24,27)(21,29,32,33)(22,25,23,28)(26,30,34,31);(3,5,7,13)(4,8,10,17)(6,15,16,12)(9,18,14,11)(20,25)(22,23)(26,33)(27,28)(29,34)(30,31);(19,21,24,32)(20,26,27,34)(22,31,23,30)(25,33,28,29);(20,27)(25,28)(26,34)(29,33)

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6255891);