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C3×AGL(1,𝔽5)×#67 #13088657

order1440
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×AGL(1,𝔽5)×#67

Splittings

FittingC22×C32×C5 ⋊ C2×C4
HallC32×C5 ⋊ C4×D4
SylowC32 ⋊ D4×AGL(1,𝔽5)
SylowC5 ⋊ C3×C4×#67

Subgroups

subgroupG/H
centerC2×C3C2×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C22×C3×C4
FrattiniC2C2×C3×D3×AGL(1,𝔽5)
FittingC22×C32×C5C2×C4
socleC2×C32×C5C22×C4
prime radicalC3×D5×#67C2
cosocleC2×C3×D5C23×C3
hypercenterC22×C3D3×AGL(1,𝔽5)
hypocenterC3×C5C3×C4×D4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C3 ◁ C22×C3

430 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 60

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#3811, C3×#72224585, C2×C3×AGL(1,𝔽5)×#67, …
maximal normal subgroup ofAGL(1,𝔽5)×#3811, C2×C3×AGL(1,𝔽5)×#67, C3×D3×D4×AGL(1,𝔽5), …
maximal quotient ofC3×#72224585, C3×AGL(1,𝔽5)×#214, C3×#11751944, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4974);