Finite Group Databasebeta

D4×D53⋊C16 #28328293

order13568
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C26

Aliases

direct productD4×D53⋊C16
unambiguous semidirect productD53⋊(D4×C16)

Splittings

SylowC53 ⋊ C2×D4×C16

Subgroups

subgroupG/H
centerC2×C8C22×#6157
commutatorC2×C53C23×C16
FrattiniC2×C4C23×#6157
FittingC8×D4×C53C4
socleC22×C53C23×C8
prime radicalC2×D4×D53C8
cosocleC2×#88322C24
hypercenterC8×D4#6157
hypocenterC53C2×D4×C16
LCSG ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C8 ◁ C8×D4

806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3392

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1113769);