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C3×#10617173 #14320561

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC3×#10617173

Splittings

FittingC3×C4×C5×D4 ⋊ C4
HallC3×C5 ⋊ #2290
SylowC5 ⋊ C3×#2290

Subgroups

subgroupG/H
centerC2×C3×C4C22×AGL(1,𝔽5)
commutatorC22×C5C23×C3×C4
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC3×C4×C5×D4C4
socleC22×C3×C5C23×C4
prime radicalC2×C3×D4×D5C22
cosocleC22×D5C24×C3
hypercenterC3×C4×D4AGL(1,𝔽5)
hypocenterC5C3×#2290
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×D4

1392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

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, 46259);