Finite Group Databasebeta

C2×#13124187 #16729549

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#13124187

Splittings

FittingC22×C13×#104 ⋊ C2
SylowC13 ⋊ C2×#3018

Subgroups

subgroupG/H
centerC2×C4#88136
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC22×C13×#104C2
socleC22×C13C2×#120
hypercenterC22×#104D13
hypocenterC13C2×#3018
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#104

4850 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, 1036198);