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C3×#10603803 #14280217

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×#10603803

Splittings

FittingC3×C5×#95 ⋊ C4
HallC3×C5 ⋊ #1443
SylowC5 ⋊ C3×#1443

Subgroups

subgroupG/H
centerC23×C3C22×AGL(1,𝔽5)
commutatorC23×C5C22×C3×C4
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC3×C5×#95C4
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C23
cosocleC23×D5C23×C3
hypercenterC3×#95AGL(1,𝔽5)
hypocenterC5C3×#1443
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#95

952 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

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, 5915);