Finite Group Databasebeta

C2×#31823354 #49097735

order35968
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#31823354

Splittings

FittingC22×C42×C281 ⋊ C2
SylowC281 ⋊ C2×#388

Subgroups

subgroupG/H
centerC24C22×D281
commutatorC22×C281C23×C4
FrattiniC23C23×D281
FittingC22×C42×C281C2
socleC24×C281C23
prime radicalC24×D281C22
cosocleC23×C281C24
hypercenterC22×C42D281
hypocenterC281C2×#388
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C24 ◁ C22×C42

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17984

Conjugacy classes & character table

9016 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35968, 6942);