Finite Group Databasebeta

C2×C22⋊(C439⋊C8) #43243565

order28096
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊(C439⋊C8)

Splittings

SylowC439 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×D439
commutatorC2×C439C22×C8
FrattiniC2×C4C22×D439
FittingC23×C4×C439C2
socleC23×C439C2×C4
prime radicalC24×C439C4
cosocleC2×C4×C439C23
hypercenterC23×C4D439
hypocenterC439C2×C22⋊C8
LCSG ▷ C2×C439 ▷ C439
UCSC1 ◁ C22×C4 ◁ C23×C4

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14048

Conjugacy classes & character table

7048 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28096, 510);