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C3×D5⋊#364 #14314409

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

Aliases

direct productC3×D5⋊#364
unambiguous semidirect productD5⋊(C3×#364)

Splittings

HallC3×C5 ⋊ C2×#364
SylowC5 ⋊ C2×C3×#364

Subgroups

subgroupG/H
centerC3×C8C4⋊AGL(1,𝔽5)
commutatorC4×C5C22×C3×C8
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C4×C5×C8C4
socleC2×C3×C5C2×C4⋊C8
prime radicalC22×C3×D5M16
cosocleC2×#168C23×C3
hypercenterC3×C4×C8AGL(1,𝔽5)
hypocenterC5C2×C3×#364
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C8 ◁ C2×C3×C8 ◁ C3×C4×C8

336 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 40107);