Finite Group Databasebeta

C2×#13130954 #16799087

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13130954
unambiguous semidirect productD13⋊#1952

Splittings

FittingC2×C13×#108 ⋊ C4
SylowC13 ⋊ C2×#1952

Subgroups

subgroupG/H
centerC22#11719083
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×#108C4
socleC22×C13#389
prime radicalC23×D13#41
cosocleC2×C4×D13C24
hypercenterC2×#108#261
hypocenterC13C2×#1952
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#108

918 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

148 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1105736);