Finite Group Databasebeta

C22×#10597322 #14576891

order2432
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC22×#10597322

Splittings

FittingC22×C42×C19 ⋊ C2
SylowC19 ⋊ C22×#126

Subgroups

subgroupG/H
centerC24C22×D19
commutator, cosocleC22×C19C25
FrattiniC22C24×D19
FittingC22×C42×C19C2
socleC24×C19C23
prime radicalC24×D19C22
hypercenterC22×C42D19
hypocenterC19C22×#126
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C24 ◁ C22×C42

1320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18073901
maximal normal subgroup of#18073901

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 17766);