Finite Group Databasebeta

← Prev (#234921) Next (#234923) →

Cayley diagram

C2×#9943 #234922

order512
nilpotency class3
isoclinismisoclinic class of #9938
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#9943

Subgroups

subgroupG/H
center, socleC23#392
commutator, Frattini, cosocleC23×C4C24
prime radicalC23×#41C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

2434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 128

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#234949
maximal normal subgroup ofC2×#234949

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 142118);