Finite Group Databasebeta

C16×C4⋊#261 #16789599

order3328
isoclinismisoclinic class of #6118
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productC16×C4⋊#261

Splittings

FittingC4×C13×C16 ⋊ C4
SylowC13 ⋊ C16×C4⋊C4

Subgroups

subgroupG/H
centerC2×C16C2×#261
commutatorC2×C13C2×C4×C16
FrattiniC2×C8C22×#261
FittingC4×C13×C16C4
socleC22×C13C2×C4×C8
prime radicalC22×D13C22×C8
cosocleC2×C8×D13C23
hypercenterC4×C16#261
hypocenterC13C16×C4⋊C4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C16 ◁ C4×C16

398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1096248);