Finite Group Databasebeta

C22⋊C4×C22⋊D19 #14566454

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

Aliases

direct productC22⋊C4×C22⋊D19

Splittings

FittingC22×C22⋊C4×C19 ⋊ C2
SylowC19 ⋊ D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D19
commutatorC22×C19C23×C4
FittingC22×C22⋊C4×C19C2
socle, cosocleC23×C19C24
prime radicalC23×C22⋊D19C2
hypercenterC22×C22⋊C4D19
hypocenterC19D4×C22⋊C4
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C22⋊C4

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, 7329);