Finite Group Databasebeta

C2×#13117013 #16017656

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

Aliases

direct productC2×#13117013

Splittings

FittingC2×C13×#364 ⋊ C2
SylowC13 ⋊ C2×#2231

Subgroups

subgroupG/H
centerC22#11718503
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C13×#364C2
socleC22×C13#476
prime radicalC2×#88158C22
hypercenterC2×#364D13
hypocenterC13C2×#2231
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#364

526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 324305);