Finite Group Databasebeta

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D4×#16860794 #44559102

order32128
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD4×#16860794

Splittings

SylowC251 ⋊ D4×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D251
commutator, socleC22×C251C23×C4
FittingC2×C4×D4×C251C2
prime radicalC22×D4×C251C4
cosocleC2×C4×C251C24
hypercenterC2×C4×D4D251
hypocenterC251D4×M16
LCSG ▷ C22×C251 ▷ C251
UCSC1 ◁ C2×C4 ◁ C2×C4×D4

544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8032

Conjugacy classes & character table

5050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32128, 13247);