Finite Group Databasebeta

C2×C4×#17985115 #49097634

order35968
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×#17985115

Splittings

FittingC22×C42×C281 ⋊ C2
SylowC281 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D281
commutatorC2×C281C22×C42
FrattiniC23C23×D281
FittingC22×C42×C281C2
socleC24×C281C23
prime radicalC24×D281C22
cosocleC23×C281C24
hypercenterC22×C42D281
hypocenterC281C2×C4×C22⋊C4
LCSG ▷ C2×C281 ▷ C281
UCSC1 ◁ C23×C4 ◁ C22×C42

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17984

Conjugacy classes & character table

9040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35968, 6841);