Finite Group Databasebeta

C2×#13116329 #15891970

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13116329

Splittings

SylowC13 ⋊ C2×#2087

Subgroups

subgroupG/H
centerC24C2×D52
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC22×C13×C4⋊C8C2
socle, prime radicalC24×C13C2×D4
hypercenterC22×C4⋊C8D13
hypocenterC13C2×#2087
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊C8

1054 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 198619);