Finite Group Databasebeta

C2×#13112956 #15777873

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#13112956

Splittings

SylowC13 ⋊ C2×#1391

Subgroups

subgroupG/H
centerC2×C4#88046
commutatorC23×C13C2×C42
FrattiniC2×#41C22×D13
FittingC2×C13×#410C2
socleC22×C13#342
prime radicalC22×C13×#41C22
cosocleC2×C13×#41C23
hypercenterC2×#410D13
hypocenterC13C2×#1391
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#410

782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 84522);