Finite Group Databasebeta

C2×#31823222 #49095008

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

Aliases

direct productC2×#31823222

Splittings

SylowC281 ⋊ C2×#339

Subgroups

subgroupG/H
centerC22×C4C22⋊D281
commutatorC4×C281C2×C42
FrattiniC22×C4C22×D281
FittingC2×#117×C281C2
socleC23×C281C22⋊C4
prime radicalC24×C281D4
cosocleC22×C4×C281C23
hypercenterC2×#117D281
hypocenterC281C2×#339
LCSG ▷ C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8992

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, 4215);