Finite Group Databasebeta

C2×D13⋊(C4⋊C16) #16806989

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

Aliases

direct productC2×D13⋊(C4⋊C16)
unambiguous semidirect productD13⋊(C2×C4⋊C16)

Splittings

SylowC13 ⋊ C22×C4⋊C16

Subgroups

subgroupG/H
centerC22×C8C2×#261
commutatorC2×C13C23×C16
FrattiniC2×C4C23×#261
FittingC2×C4×C8×C13C4
socleC23×C13C22×C8
prime radicalC23×D13C2×C8
cosocleC2×#1055C24
hypercenterC2×C4×C8#261
hypocenterC13C22×C4⋊C16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113638);