Finite Group Databasebeta

Q8×D13⋊C16 #16807247

order3328
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C25

Aliases

direct productQ8×D13⋊C16
unambiguous semidirect productD13⋊(Q8×C16)

Splittings

SylowC13 ⋊ C2×Q8×C16

Subgroups

subgroupG/H
centerC2×C8C22×#261
commutatorC2×C13C23×C16
FrattiniC2×C4C23×#261
FittingC8×Q8×C13C4
socleC22×C13C23×C8
prime radicalC22×D13C22×C8
cosocleC2×#1055C24
hypercenterC8×Q8#261
hypocenterC13C2×Q8×C16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C8×Q8

582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113896);