Finite Group Databasebeta

Q16×#6127 #16744389

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productQ16×#6127

Splittings

FittingC2×C4×C13×Q16 ⋊ C2
SylowC13 ⋊ Q16×#41

Subgroups

subgroupG/H
centerC2×C4C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C4×C13×Q16C2
socleC22×C13C23×D4
prime radicalC2×#6127D4
hypercenterC2×C4×Q16D13
hypocenterC13Q16×#41
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q16

1826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1051038);