Finite Group Databasebeta

C22×C4×#6127 #16769493

order3328
isoclinismisoclinic class of Dic26
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC22×C4×#6127

Splittings

FittingC23×C42×C13 ⋊ C2
SylowC13 ⋊ C22×C4×#41

Subgroups

subgroupG/H
centerC22×C42C2×D13
commutatorC2×C13C25×C4
FrattiniC22C25×D13
FittingC23×C42×C13C2
socleC24×C13C24
prime radicalC23×#6127C2
cosocleC22×C13C26
hypercenterC23×C42D13
hypocenterC13C22×C4×#41
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C42 ◁ C23×C42

12878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 1076142);