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C5×C3⋊(C31⋊AGL(1,𝔽5)) #22604904

order9300
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊(C31⋊AGL(1,𝔽5))
unambiguous semidirect productC3⋊(C5×C31⋊AGL(1,𝔽5))

Splittings

Fitting, socle, HallC3×C52×C31 ⋊ C4
derivedC3×C5×C31 ⋊ C4×C5
HallC52×C31 ⋊ Dic3
HallC3×C31 ⋊ C5×AGL(1,𝔽5)
HallC3×C52 ⋊ Dic31
SylowC31 ⋊ C5×ΓL(1,𝔽16)
SylowC52 ⋊ Dic93
SylowC3 ⋊ C5×C31⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C31⋊AGL(1,𝔽5))
commutator, hypocenterC3×C5×C31C4×C5
FrattiniC1G
Fitting, socleC3×C52×C31C4
LCSG ▷ C3×C5×C31
UCSC1 ◁ C5

52 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

945 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C9⋊(C31⋊AGL(1,𝔽5)), C5×C3⋊((C31⋊C3)⋊AGL(1,𝔽5)), C3×C5×C3⋊(C31⋊AGL(1,𝔽5)), …
maximal normal subgroup ofC5×C3⋊((C31⋊C3)⋊AGL(1,𝔽5)), C3×C5×C3⋊(C31⋊AGL(1,𝔽5))
maximal quotient ofC5×C9⋊(C31⋊AGL(1,𝔽5)), C3×C5×C3⋊(C31⋊AGL(1,𝔽5)), C5×C3⋊(C3⋊(C31⋊AGL(1,𝔽5)))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9300, 178);