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C3×C151⋊AGL(1,𝔽5) #22583702

order9060
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×C151⋊AGL(1,𝔽5)

Splittings

Fitting, socle, HallC3×C5×C151 ⋊ C4
derived, HallC5×C151 ⋊ C3×C4
HallC3×C151 ⋊ AGL(1,𝔽5)
SylowC151 ⋊ C3×AGL(1,𝔽5)
HallC3×C5 ⋊ Dic151
SylowC5 ⋊ C3×Dic151

Subgroups

subgroupG/H
center, hypercenterC3C151⋊AGL(1,𝔽5)
commutator, hypocenterC5×C151C3×C4
FrattiniC1G
Fitting, socleC3×C5×C151C4
LCSG ▷ C5×C151
UCSC1 ◁ C3

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

915 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C151⋊C9)⋊AGL(1,𝔽5), C9×C151⋊AGL(1,𝔽5), C3×(C151⋊C3)⋊AGL(1,𝔽5), …
maximal normal subgroup of(C151⋊C9)⋊AGL(1,𝔽5), C9×C151⋊AGL(1,𝔽5), C3×(C151⋊C3)⋊AGL(1,𝔽5), …
maximal quotient ofC9×C151⋊AGL(1,𝔽5), C32×C151⋊AGL(1,𝔽5), C3×C3⋊(C151⋊AGL(1,𝔽5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9060, 36);