Finite Group Databasebeta

C4×#10597375 #14566157

order2432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#10597375

Splittings

FittingC22×C42×C19 ⋊ C2
SylowC19 ⋊ C4×#123

Subgroups

subgroupG/H
centerC22×C4C22×D19
commutatorC22×C19C23×C4
FrattiniC23C23×D19
FittingC22×C42×C19C2
socle, cosocleC23×C19C24
prime radicalC22×C22⋊D19C22
hypercenterC22×C42D19
hypocenterC19C4×#123
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C22×C42

688 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#18077226, #18077236
maximal normal subgroup of#18077226, #18077236

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 7032);