Finite Group Databasebeta

C2×#13115622 #15866466

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

Aliases

direct productC2×#13115622

Splittings

SylowC13 ⋊ C2×#1952

Subgroups

subgroupG/H
centerC23#88149
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC22×C13×#108C2
socleC23×C13#121
prime radicalC24×C13#41
cosocleC22×C4×C13C24
hypercenterC22×#108D13
hypocenterC13C2×#1952
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#108

918 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 173115);