Finite Group Databasebeta

C4×(C22⋊D19)⋊C4 #14565979

order2432
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×(C22⋊D19)⋊C4

Splittings

FittingC4×C22⋊C4×C19 ⋊ C2
SylowC19 ⋊ C42×D4

Subgroups

subgroupG/H
centerC22×C4C22×D19
commutatorC2×C19C22×C42
FrattiniC23C23×D19
FittingC4×C22⋊C4×C19C2
socle, cosocleC23×C19C24
prime radicalC22×C22⋊D19C22
hypercenterC4×C22⋊C4D19
hypocenterC19C42×D4
LCSG ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

924 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 6854);