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C5×C3⋊(C19⋊AGL(1,𝔽5)) #19152866

order5700
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊(C19⋊AGL(1,𝔽5))
unambiguous semidirect productC3⋊(C5×C19⋊AGL(1,𝔽5))
unambiguous semidirect productC19⋊(C5×ΓL(1,𝔽16))

Splittings

Fitting, socle, HallC3×C52×C19 ⋊ C4
derivedC3×C5×C19 ⋊ C4×C5
HallC52×C19 ⋊ Dic3
HallC3×C52 ⋊ Dic19
HallC3×C19 ⋊ C5×AGL(1,𝔽5)
SylowC52 ⋊ Dic57
SylowC19 ⋊ C5×ΓL(1,𝔽16)
SylowC3 ⋊ C5×C19⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C19⋊AGL(1,𝔽5))
commutator, hypocenterC3×C5×C19C4×C5
FrattiniC1G
Fitting, socleC3×C52×C19C4
LCSG ▷ C3×C5×C19
UCSC1 ◁ C5

52 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

585 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C9⋊(C19⋊AGL(1,𝔽5)), C5×C3⋊((C19⋊C3)⋊AGL(1,𝔽5)), C3×C5×C3⋊(C19⋊AGL(1,𝔽5)), …
maximal normal subgroup ofC5×C3⋊((C19⋊C3)⋊AGL(1,𝔽5)), C3×C5×C3⋊(C19⋊AGL(1,𝔽5))
maximal quotient ofC5×C9⋊(C19⋊AGL(1,𝔽5)), C3×C5×C3⋊(C19⋊AGL(1,𝔽5)), C5×C3⋊(C3⋊(C19⋊AGL(1,𝔽5)))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 123);