Finite Group Databasebeta

C2×#13123316 #16726416

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#13123316

Splittings

FittingC22×C13×#101 ⋊ C2
SylowC13 ⋊ C2×#2889

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC22×C13×#101C2
socleC22×C13C22×C22⋊C4
prime radicalC22×#88254C2
cosocleC2×C4×C13C25
hypercenterC22×#101D13
hypocenterC13C2×#2889
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#101

4770 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033065);