Finite Group Databasebeta

C2×#13115347 #15864845

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#13115347

Splittings

FittingC22×C13×#102 ⋊ C2
SylowC13 ⋊ C2×#1907

Subgroups

subgroupG/H
centerC23#88192
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC22×C13×#102C2
socleC23×C13#121
prime radicalC22×#88186C2
cosocleC22×C4×C13C24
hypercenterC22×#102D13
hypocenterC13C2×#1907
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

1826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 171494);