Finite Group Databasebeta

C2×#13115324 #15864802

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#13115324

Splittings

FittingC2×C13×H(3,ℤ/4) ⋊ C2
SylowC13 ⋊ C2×#1904

Subgroups

subgroupG/H
centerC22#11718326
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×H(3,ℤ/4)C2
socleC22×C13#386
prime radicalC22×#88162C2
cosocleC22×C4×C13C24
hypercenterC2×H(3,ℤ/4)D13
hypocenterC13C2×#1904
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

1894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 171451);