Finite Group Databasebeta

C2×C42×Dic26 #16021115

order3328
isoclinismisoclinic class of Dic26
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×C42×Dic26

Splittings

SylowC13 ⋊ C2×C42×Q8

Subgroups

subgroupG/H
centerC22×C42C2×D13
commutatorC2×C13C23×C42
FrattiniC23C24×D13
FittingC2×C43×C13C2
socle, prime radicalC24×C13C24
cosocleC23×C13C25
hypercenterC2×C43D13
hypocenterC13C2×C42×Q8
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C42 ◁ C2×C43

3966 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 327764);