Finite Group Databasebeta

C2×#31823227 #49095026

order35968
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#31823227

Splittings

SylowC281 ⋊ C2×#341

Subgroups

subgroupG/H
centerC22×C4C22⋊D281
commutatorC4×C281C2×C42
FrattiniC22×C4C22×D281
FittingC22×M16×C281C2
socleC23×C281C4⋊C4
prime radicalC24×C281Q8
cosocleC22×C4×C281C23
hypercenterC22×M16D281
hypocenterC281C2×#341
LCSG ▷ C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×M16

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17984

Conjugacy classes & character table

5656 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35968, 4233);