Finite Group Databasebeta

C4×#22548698 #44552887

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

Aliases

direct productC4×#22548698

Splittings

FittingC22×C42×C251 ⋊ C2
SylowC251 ⋊ C4×#123

Subgroups

subgroupG/H
centerC22×C4C22×D251
commutatorC22×C251C23×C4
FrattiniC23C23×D251
FittingC22×C42×C251C2
socle, cosocleC23×C251C24
prime radicalC22×C22⋊D251C22
hypercenterC22×C42D251
hypocenterC251C4×#123
LCSG ▷ C22×C251 ▷ C251
UCSC1 ◁ C22×C4 ◁ C22×C42

688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16064

Conjugacy classes & character table

8056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32128, 7032);