Finite Group Databasebeta

C2×#13114983 #15863182

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13114983

Splittings

SylowC13 ⋊ C2×#1841

Subgroups

subgroupG/H
centerC2×C4#88126
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×H(3,ℤ/4)C2
socleC22×C13#383
prime radicalC24×C13#41
cosocleC22×C4×C13C24
hypercenterC2×H(3,ℤ/4)D13
hypocenterC13C2×#1841
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ C2×H(3,ℤ/4)

730 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 169831);