Finite Group Databasebeta

C2×#13113128 #15828522

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#13113128

Splittings

SylowC13 ⋊ C2×#1452

Subgroups

subgroupG/H
centerC2×C42C22×D13
commutatorC22×C13C22×C42
FrattiniC42C23×D13
FittingC22×C4×C8×C13C2
socleC23×C13C2×C42
prime radicalC24×C13C42
cosocleC42×C13C24
hypercenterC22×C4×C8D13
hypocenterC13C2×#1452
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C42 ◁ C22×C4×C8

902 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 135171);