Finite Group Databasebeta

C2×#13131244 #16807225

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

Aliases

direct productC2×#13131244

Splittings

FittingC2×C13×Q32 ⋊ C4
SylowC13 ⋊ C2×#2180

Subgroups

subgroupG/H
centerC22#11719102
commutatorC8×C13C23×C4
FrattiniC8C23×#261
FittingC2×C13×Q32C4
socleC22×C13#442
prime radicalC2×#88173C22
cosocleC8×D13C24
hypercenterC2×Q32#261
hypocenterC13C2×#2180
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113874);