Finite Group Databasebeta

C3×D5⋊(C22⋊C16) #14312802

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C16 · Schur multiplier (H2) = C24

Aliases

direct productC3×D5⋊(C22⋊C16)
unambiguous semidirect productD5⋊(C3×C22⋊C16)

Splittings

HallC3×C5 ⋊ C2×C22⋊C16
SylowC5 ⋊ C2×C3×C22⋊C16

Subgroups

subgroupG/H
centerC2×C3×C8C2×AGL(1,𝔽5)
commutatorC2×C5C22×C3×C16
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC22×C3×C5×C8C4
socleC22×C3×C5C22×C8
prime radicalC23×C3×D5C8
cosocleC2×#168C23×C3
hypercenterC22×C3×C8AGL(1,𝔽5)
hypocenterC5C2×C3×C22⋊C16
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C8 ◁ C22×C3×C8

544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 38500);