Finite Group Databasebeta

C2×#13115542 #15865655

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#13115542

Splittings

SylowC13 ⋊ C2×#1937

Subgroups

subgroupG/H
centerC22×C4D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#416C2
socleC23×C13C4×D4
prime radicalC22×C13×#41C22
cosocleC22×C4×C13C24
hypercenterC2×#416D13
hypocenterC13C2×#1937
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

1114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 172304);