Finite Group Databasebeta

C2×#13115502 #15865497

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#13115502

Splittings

SylowC13 ⋊ C2×#1932

Subgroups

subgroupG/H
centerC2×C4#88192
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC22×C13×#104C2
socleC22×C13#388
prime radicalC22×C13×#41C22
cosocleC22×C4×C13C24
hypercenterC22×#104D13
hypocenterC13C2×#1932
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#104

1046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 172146);