Finite Group Databasebeta

C2×#31823358 #49097751

order35968
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#31823358

Splittings

SylowC281 ⋊ C2×#389

Subgroups

subgroupG/H
centerC24C22×D281
commutatorC22×C281C23×C4
FrattiniC23C23×D281
FittingC22×C4⋊C4×C281C2
socle, prime radicalC24×C281C23
cosocleC23×C281C24
hypercenterC22×C4⋊C4D281
hypocenterC281C2×#389
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C24 ◁ C22×C4⋊C4

800 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 35968

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, 6958);