Finite Group Databasebeta

C2×#13131183 #16807021

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

Aliases

direct productC2×#13131183

Splittings

FittingC22×C13×C16 ⋊ C4
SylowC13 ⋊ C2×#2155

Subgroups

subgroupG/H
centerC2×C4#88101
commutatorC8×C13C23×C4
FrattiniC8C23×#261
FittingC22×C13×C16C4
socleC22×C13C2×#106
prime radicalC23×D13SD16
cosocleC8×D13C24
hypercenterC22×C16#261
hypocenterC13C2×#2155
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

658 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113670);