Finite Group Databasebeta

C2×#31823297 #49097595

order35968
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C22

Aliases

direct productC2×#31823297

Splittings

SylowC281 ⋊ C2×M64

Subgroups

subgroupG/H
centerC2×C16C2×D281
commutatorC2×C281C22×C16
FrattiniC16C22×D281
FittingC22×C16×C281C2
socleC22×C281C2×C16
prime radicalC23×C281C16
cosocleC16×C281C23
hypercenterC22×C16D281
hypocenterC281C2×M64
LCSG ▷ C2×C281 ▷ C281
UCSC1 ◁ C2×C16 ◁ C22×C16

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17984

Conjugacy classes & character table

9040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35968, 6802);