Finite Group Databasebeta

← Prev (#49130069) Next (#49130071) →

C4×#22583637 #49130070

order36224
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#22583637

Splittings

FittingC4×SD16×C283 ⋊ C2
SylowC283 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C4D4×D283
commutatorC4×C283C23×C4
FrattiniC2×C4C23×D283
FittingC4×SD16×C283C2
socleC22×C283C22×D4
prime radicalC2×#22583637C2
cosocleC2×C4×C283C24
hypercenterC4×SD16D283
hypocenterC283C4×AGL(1,ℤ/8)
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9056

Conjugacy classes & character table

3992 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36224, 13319);