Finite Group Databasebeta

C2×#31823301 #49097604

order35968
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#31823301

Splittings

SylowC281 ⋊ C2×SD64

Subgroups

subgroupG/H
centerC22#22582820
commutator, cosocleC16×C281C23
FrattiniC16C22×D281
Fitting, prime radicalC2×D16×C281C2
socleC22×C281D16
hypercenterC2×D16D281
hypocenterC281C2×SD64
LCSG ▷ C16×C281 ▷ C8×C281 ▷ C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×D16

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17984

Conjugacy classes & character table

3118 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35968, 6811);