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C19×C3⋊(C3⋊(C7⋊AGL(1,𝔽5))) #37561596

order23940
automorphism?
homologyAbelianization (H1) = C4×C19 · Schur multiplier (H2) = C3

Aliases

direct productC19×C3⋊(C3⋊(C7⋊AGL(1,𝔽5)))
unambiguous semidirect productC3⋊(C19×C3⋊(C7⋊AGL(1,𝔽5)))
unambiguous semidirect productC7⋊(C19×C3⋊ΓL(1,𝔽16))

Splittings

Fitting, socle, HallC32×C5×C7×C19 ⋊ C4
derived, HallC32×C5×C7 ⋊ C4×C19
HallC32×C7×C19 ⋊ AGL(1,𝔽5)
HallC32×C5×C19 ⋊ Dic7
HallC5×C7×C19 ⋊ C3⋊Dic3
HallC32×C19 ⋊ C7⋊AGL(1,𝔽5)
HallC7×C19 ⋊ C3⋊ΓL(1,𝔽16)
HallC5×C19 ⋊ C3⋊Dic21
HallC32×C7 ⋊ C19×AGL(1,𝔽5)
HallC32×C5 ⋊ C19×Dic7
HallC5×C7 ⋊ C19×C3⋊Dic3
SylowC32 ⋊ C19×C7⋊AGL(1,𝔽5)
SylowC7 ⋊ C19×C3⋊ΓL(1,𝔽16)
SylowC5 ⋊ C19×C3⋊Dic21

Subgroups

subgroupG/H
center, hypercenterC19C3⋊(C3⋊(C7⋊AGL(1,𝔽5)))
commutator, hypocenterC32×C5×C7C4×C19
FrattiniC1G
Fitting, socleC32×C5×C7×C19C4
prime radicalC32×C7×D5×C19C2
cosocleC32×C7×D5C2×C19
LCSG ▷ C32×C5×C7
UCSC1 ◁ C19

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5985

Conjugacy classes & character table

2451 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 728);