Finite Group Databasebeta

← Prev (#607748) Next (#607750) →

Cayley diagram

C2×#14809 #607749

order512
nilpotency class2
isoclinismisoclinic class of #14715
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14809

Subgroups

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

3998 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)(11,12,15,13)(14,17,18,16)(19,20,23,26)(21,25,22,24);(8,10)(12,13)(16,17)(19,21,23,22)(20,24,26,25);(7,8)(9,10)(11,13,15,12)(14,17,18,16)(19,22,23,21)(20,25,26,24);(3,4)(5,6)(11,14,15,18)(12,16,13,17)(19,20)(21,24)(22,25)(23,26)

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, 514945);