Finite Group Databasebeta

← Prev (#7637126) Next (#7637128) →

Cayley diagram

C2×#39170 #7637127

order512
nilpotency class2
isoclinismisoclinic class of #37644
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#39170

Subgroups

subgroupG/H
center, socle, prime radicalC24C25
commutator, Frattini, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

6874 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 6 generators on 30 points:

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

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, 7544323);