Finite Group Databasebeta

C2×#13127972 #16769425

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13127972

Splittings

FittingC22×C13×M32 ⋊ C2
SylowC13 ⋊ C2×#3414

Subgroups

subgroupG/H
centerC2×C4C2×D104
commutator, cosocleC8×C13C25
FrattiniC8C24×D13
FittingC22×C13×M32C2
socleC22×C13C22×D8
hypercenterC22×M32D13
hypocenterC13C2×#3414
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ C22×M32

2098 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 1076074);