Finite Group Databasebeta

Q16×D13⋊C8 #16795182

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productQ16×D13⋊C8
unambiguous semidirect productD13⋊(C8×Q16)

Splittings

SylowC13 ⋊ C2×C8×Q16

Subgroups

subgroupG/H
centerC2×C4D4×#261
commutatorC4×C13C23×C8
FrattiniC2×C4C23×#261
FittingC4×C13×Q16C4
socleC22×C13C2×C4×D4
prime radicalC22×D13C4×D4
cosocleC4×Dic13C24
hypercenterC4×Q16#261
hypocenterC13C2×C8×Q16
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q16

734 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1101831);