Finite Group Databasebeta

C2×C16×D52 #16016070

order3328
isoclinismisoclinic class of Dic26
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C26

Aliases

direct productC2×C16×D52

Splittings

FittingC2×C4×C13×C16 ⋊ C2
SylowC13 ⋊ C2×D4×C16

Subgroups

subgroupG/H
centerC22×C16C2×D13
commutatorC2×C13C23×C16
FrattiniC2×C8C23×D13
FittingC2×C4×C13×C16C2
socleC23×C13C22×C8
prime radicalC22×D52C8
cosocleC2×C8×C13C24
hypercenterC2×C4×C16D13
hypocenterC13C2×D4×C16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C16 ◁ C2×C4×C16

806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322719);