Finite Group Databasebeta

← Prev (#14314292) Next (#14314294) →

D15×C4⋊C16 #14314293

order1920
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productD15×C4⋊C16

Splittings

FittingC3×C5×C4⋊C16 ⋊ C2
HallC3×C5 ⋊ C2×C4⋊C16
SylowC5 ⋊ D3×C4⋊C16
SylowC3 ⋊ D5×C4⋊C16

Subgroups

subgroupG/H
center, FrattiniC2×C8C22×D15
commutatorC2×C3×C5C22×C16
FittingC3×C5×C4⋊C16C2
socleC22×C3×C5C22×C8
prime radicalC22×D15C2×C8
cosocleC2×C3×C5×C8C23
hypercenterC4⋊C16D15
hypocenterC3×C5C2×C4⋊C16
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C8 ◁ C4⋊C16

368 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 39991);