Finite Group Databasebeta

D4×C4⋊Dic19 #14566537

order2432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×C4⋊Dic19

Splittings

SylowC19 ⋊ D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D19
commutatorC22×C19C23×C4
FittingC2×C4×D4×C19C2
socle, cosocleC23×C19C24
prime radicalC22×D4×C19C22
hypercenterC2×C4×D4D19
hypocenterC19D4×C4⋊C4
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C4×D4

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18076697, #18076701, #18076725, …
maximal normal subgroup of#18076697, #18076701, #18076725, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 7412);