Finite Group Databasebeta

D4×#64520 #14572372

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

Aliases

direct productD4×#64520

Splittings

SylowC19 ⋊ D4×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D19
commutator, socleC22×C19C23×C4
FittingC2×C4×D4×C19C2
prime radicalC22×D4×C19C4
cosocleC2×C4×C19C24
hypercenterC2×C4×D4D19
hypocenterC19D4×M16
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C4×D4

544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 608

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18076865, #18076869, #18076879, …
maximal normal subgroup of#18076865, #18076869, #18076879, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 13247);