Finite Group Databasebeta

C2×#31823303 #49097607

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

Aliases

direct productC2×#31823303

Splittings

SylowC281 ⋊ C2×Q64

Subgroups

subgroupG/H
centerC22#22582820
commutator, cosocleC16×C281C23
FrattiniC16C22×D281
FittingC2×Q32×C281C2
socle, prime radicalC22×C281D16
hypercenterC2×Q32D281
hypocenterC281C2×Q64
LCSG ▷ C16×C281 ▷ C8×C281 ▷ C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×Q32

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 35968

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, 6814);