Finite Group Databasebeta

← Prev (#6628962) Next (#6628964) →

Cayley diagram

C2×#32924 #6628963

order512
nilpotency class3
isoclinismisoclinic class of #32888
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#32924

Subgroups

subgroupG/H
center, socleC23C2×#120
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#453C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

5020 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 64

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#6628968
maximal normal subgroup ofC2×#6628968

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6536159);