Finite Group Databasebeta

D4×(C2×D19)⋊C4 #14566452

order2432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD4×(C2×D19)⋊C4

Splittings

FittingC2×C4×D4×C19 ⋊ C2
SylowC19 ⋊ D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D19
commutatorC22×C19C23×C4
FittingC2×C4×D4×C19C2
socle, cosocleC23×C19C24
prime radicalC22×D4×D19C2
hypercenterC2×C4×D4D19
hypocenterC19D4×C22⋊C4
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C4×D4

1252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 608

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 7327);