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C3×D5⋊#349 #14312907

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23

Aliases

direct productC3×D5⋊#349
unambiguous semidirect productD5⋊(C3×#349)

Splittings

HallC3×C5 ⋊ C2×#349
SylowC5 ⋊ C2×C3×#349

Subgroups

subgroupG/H
centerC3×C4C2×C22⋊AGL(1,𝔽5)
commutatorC22×C5C22×C3×C8
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×M16C4
socleC2×C3×C5C2×C22⋊C8
prime radicalC23×C3×D5C8
cosocleC2×#168C23×C3
hypercenterC2×C3×M16AGL(1,𝔽5)
hypocenterC5C2×C3×#349
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C2×C3×C8 ◁ C2×C3×M16

472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 38605);