Finite Group Databasebeta

C2×#13116939 #16017365

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

Aliases

direct productC2×#13116939

Splittings

FittingC22×C13×M32 ⋊ C2
SylowC13 ⋊ C2×#2218

Subgroups

subgroupG/H
centerC23C2×D104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC22×C13×M32C2
socleC23×C13C2×D8
hypercenterC22×M32D13
hypocenterC13C2×#2218
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×M32

786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 324014);