Finite Group Databasebeta

C2×#13113120 #15828498

order3328
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C8

Aliases

direct productC2×#13113120

Splittings

SylowC13 ⋊ C2×#1450

Subgroups

subgroupG/H
centerC2×C42C22×D13
commutatorC2×C13C22×C4×C8
FrattiniC42C23×D13
FittingC2×C13×#431C2
socleC23×C13C2×C42
prime radicalC24×C13C42
cosocleC42×C13C24
hypercenterC2×#431D13
hypocenterC13C2×#1450
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C42 ◁ C2×#431

982 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 135147);