Finite Group Databasebeta

C4×#10597336 #14566193

order2432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC4×#10597336

Splittings

SylowC19 ⋊ C4×#125

Subgroups

subgroupG/H
centerC22×C4C22×D19
commutatorC22×C19C23×C4
FrattiniC23C23×D19
FittingC4×C4⋊C4×C19C2
socle, prime radical, cosocleC23×C19C24
hypercenterC4×C4⋊C4D19
hypocenterC19C4×#125
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2432

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18082526, #18082528, #18082531, …
maximal normal subgroup of#18082526, #18082528, #18082531, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 7068);