Finite Group Databasebeta

C2×#13116115 #15890756

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13116115

Splittings

FittingC22×C13×#101 ⋊ C2
SylowC13 ⋊ C2×#2049

Subgroups

subgroupG/H
centerC22#11718622
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC22×C13×#101C2
socleC22×C13#394
prime radicalC22×#6127C22
hypercenterC22×#101D13
hypocenterC13C2×#2049
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#101

1322 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 197405);