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C3×#10604994 #14284192

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×#10604994

Splittings

HallC3×C5 ⋊ #1530
SylowC5 ⋊ C3×#1530

Subgroups

subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×#41C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66166C2
cosocleC4×Dic5C23×C3
hypercenterC2×C3×#41AGL(1,𝔽5)
hypocenterC5C3×#1530
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#41

512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 9890);