Finite Group Databasebeta

C2×#13123638 #16726974

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13123638

Splittings

FittingC22×C13×#97 ⋊ C2
SylowC13 ⋊ C2×#2943

Subgroups

subgroupG/H
centerC22×C4C2×D52
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC22×C13×#97C2
socleC23×C13C22×D4
prime radicalC22×#88158C2
cosocleC2×C4×C13C25
hypercenterC22×#97D13
hypocenterC13C2×#2943
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×#97

2854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033623);