Finite Group Databasebeta

C2×#13125184 #16732148

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C27×C4

Aliases

direct productC2×#13125184

Splittings

FittingC2×C13×#533 ⋊ C2
SylowC13 ⋊ C2×#3135

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#533C2
socleC23×C13C22×D4
prime radicalC2×#11719182C2
hypercenterC2×#533D13
hypocenterC13C2×#3135
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#533

2182 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, 1038797);