Finite Group Databasebeta

C16×#6131 #16016437

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

Aliases

direct productC16×#6131

Splittings

FittingQ8×C13×C16 ⋊ C2
SylowC13 ⋊ C16×#41

Subgroups

subgroupG/H
centerC2×C16C22×D13
commutatorC2×C13C23×C16
FrattiniC2×C8C23×D13
FittingQ8×C13×C16C2
socleC22×C13C23×C8
prime radicalC2×#6131C8
cosocleC2×C8×C13C24
hypercenterQ8×C16D13
hypocenterC13C16×#41
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C16 ◁ Q8×C16

602 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 323086);