Finite Group Databasebeta

C2×#13115376 #15864928

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#13115376

Splittings

FittingC22×C13×#99 ⋊ C2
SylowC13 ⋊ C2×#1913

Subgroups

subgroupG/H
centerC22#11718619
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC22×C13×#99C2
socleC22×C13#386
prime radicalC2×#11719509C2
cosocleC24×C13C24
hypercenterC22×#99D13
hypocenterC13C2×#1913
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C25 ◁ C22×#99

2078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 171577);