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C3×#10605015 #14297189

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

Aliases

direct productC3×#10605015

Splittings

FittingC3×C5×H(5,𝔽2) ⋊ C4
HallC3×C5 ⋊ #1792
SylowC5 ⋊ C3×#1792

Subgroups

subgroupG/H
centerC2×C3#65800
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×H(5,𝔽2)C4
socleC2×C3×C5#379
prime radicalC3×D5×H(5,𝔽2)C2
cosocleC2×C4×D5C23×C3
hypercenterC3×H(5,𝔽2)AGL(1,𝔽5)
hypocenterC5C3×#1792
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×H(5,𝔽2)

1240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

147 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽5)×#453, D3×#10605015, #72229797, …
maximal normal subgroup ofC3×AGL(1,𝔽5)×#453, D3×#10605015, #72229797

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 22887);