Finite Group Databasebeta

C2×#31823239 #49096893

order35968
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#31823239

Splittings

SylowC281 ⋊ C2×#346

Subgroups

subgroupG/H
centerC22×C8C2×D281
commutatorC2×C281C2×C4×C8
FrattiniC2×C8C22×D281
FittingC2×C4×C8×C281C2
socle, prime radicalC23×C281C2×C8
cosocleC2×C8×C281C23
hypercenterC2×C4×C8D281
hypocenterC281C2×#346
LCSG ▷ C2×C281 ▷ C281
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 35968

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, 6100);