Finite Group Databasebeta

C2×#13117129 #16021027

order3328
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13117129

Splittings

FittingC22×C13×C32 ⋊ C2
SylowC13 ⋊ C2×#2258

Subgroups

subgroupG/H
centerC2×C32C2×D13
commutatorC2×C13C23×C16
FrattiniC16C23×D13
FittingC22×C13×C32C2
socleC22×C13C22×C16
prime radicalC2×#6127C8
cosocleC13×C16C24
hypercenterC22×C32D13
hypocenterC13C2×#2258
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C32 ◁ C22×C32

470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 327676);