Finite Group Databasebeta

← Prev (#44558773) Next (#44558775) →

C2×C4×#16860794 #44558774

order32128
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×C4×#16860794

Splittings

SylowC251 ⋊ C2×C4×M16

Subgroups

subgroupG/H
centerC2×C42C2×D251
commutatorC2×C251C22×C42
FrattiniC2×C4C23×D251
FittingC22×C42×C251C2
socleC23×C251C22×C4
prime radicalC24×C251C2×C4
cosocleC2×C4×C251C24
hypercenterC22×C42D251
hypocenterC251C2×C4×M16
LCSG ▷ C2×C251 ▷ C251
UCSC1 ◁ C2×C42 ◁ C22×C42

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16064

Conjugacy classes & character table

8080 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32128, 12919);