Finite Group Databasebeta

← Prev (#6353638) Next (#6353640) →

Cayley diagram

C2×#19168 #6353639

order512
nilpotency class3
isoclinismisoclinic class of #19162
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#19168

Subgroups

subgroupG/H
center, socleC23C2×#121
commutator, Frattini, cosocleC42C25
prime radicalC2×#3100C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

2042 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#6354079
maximal normal subgroup ofC2×#6354079

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6260835);