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C3×D5⋊#368 #14314674

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productC3×D5⋊#368
unambiguous semidirect productD5⋊(C3×#368)

Splittings

HallC3×C5 ⋊ C2×#368
SylowC5 ⋊ C2×C3×#368

Subgroups

subgroupG/H
centerC3×C4#3994
commutatorC5×C8C22×C3×C4
FrattiniC8C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C16C4
socleC2×C3×C5C2×#107
prime radicalC22×C3×D5Q16
cosocleC8×D5C23×C3
hypercenterC2×C3×C16AGL(1,𝔽5)
hypocenterC5C2×C3×#368
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C2×C3×C16

288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 40372);