Finite Group Databasebeta

C16×#6101 #15778262

order3328
isoclinismisoclinic class of Dic26
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productC16×#6101

Splittings

SylowC13 ⋊ C16×C4⋊C4

Subgroups

subgroupG/H
centerC22×C16C2×D13
commutatorC2×C13C2×C4×C16
FrattiniC22×C8C22×D13
FittingC2×C4×C13×C16C2
socle, prime radicalC23×C13C22×C8
cosocleC22×C8×C13C23
hypercenterC2×C4×C16D13
hypocenterC13C16×C4⋊C4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C16 ◁ C2×C4×C16

398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 84911);