Finite Group Databasebeta

C2×#13114252 #15845295

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

Aliases

direct productC2×#13114252

Splittings

FittingC2×C8×Q8×C13 ⋊ C2
SylowC13 ⋊ C2×#1678

Subgroups

subgroupG/H
centerC23#88184
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C8×Q8×C13C2
socleC23×C13#121
prime radicalC2×#88128C22
hypercenterC2×C8×Q8D13
hypocenterC13C2×#1678
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C8×Q8

722 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 151944);