Finite Group Databasebeta

C4×Dic439⋊C4 #43243457

order28096
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×Dic439⋊C4

Splittings

SylowC439 ⋊ C4×C4⋊C4

Subgroups

subgroupG/H
centerC22×C4C2×D439
commutatorC2×C439C2×C42
FrattiniC23C22×D439
FittingC2×C42×C439C2
socle, prime radical, cosocleC23×C439C23
hypercenterC2×C42D439
hypocenterC439C4×C4⋊C4
LCSG ▷ C2×C439 ▷ C439
UCSC1 ◁ C22×C4 ◁ C2×C42

194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28096

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, 402);