Finite Group Databasebeta

C22×#10597347 #14578339

order2432
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×#10597347

Splittings

FittingC23×C8×C19 ⋊ C2
SylowC19 ⋊ C22×#131

Subgroups

subgroupG/H
centerC22×C8C2×D19
commutatorC2×C19C24×C4
FrattiniC4C24×D19
FittingC23×C8×C19C2
socleC23×C19C22×C4
prime radicalC22×#64541C2
cosocleC4×C19C25
hypercenterC23×C8D19
hypocenterC19C22×#131
LCSG ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C8 ◁ C23×C8

1504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18087950, #18087954, #18087972, …
maximal normal subgroup of#18087950, #18087954, #18087972, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 19214);