Finite Group Databasebeta

C2×#31823378 #49098507

order35968
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#31823378

Splittings

FittingC22×C22⋊C4×C281 ⋊ C2
SylowC281 ⋊ C2×#394

Subgroups

subgroupG/H
centerC24C22×D281
commutator, cosocleC23×C281C24
FrattiniC23C23×D281
FittingC22×C22⋊C4×C281C2
socleC24×C281C23
prime radicalC23×C22⋊D281C2
hypercenterC22×C22⋊C4D281
hypocenterC281C2×#394
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C24 ◁ C22×C22⋊C4

1252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17984

Conjugacy classes & character table

5644 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35968, 7714);