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C7×C3⋊(C3⋊(C19⋊AGL(1,𝔽5))) #37561595

order23940
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C3

Aliases

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

Splittings

Fitting, socle, HallC32×C5×C7×C19 ⋊ C4
derived, HallC32×C5×C19 ⋊ C4×C7
HallC32×C7×C19 ⋊ AGL(1,𝔽5)
HallC5×C7×C19 ⋊ C3⋊Dic3
HallC32×C5×C7 ⋊ Dic19
HallC32×C19 ⋊ C7×AGL(1,𝔽5)
HallC7×C19 ⋊ C3⋊ΓL(1,𝔽16)
HallC5×C19 ⋊ C7×C3⋊Dic3
HallC32×C7 ⋊ C19⋊AGL(1,𝔽5)
HallC32×C5 ⋊ C7×Dic19
HallC5×C7 ⋊ C3⋊Dic57
SylowC19 ⋊ C7×C3⋊ΓL(1,𝔽16)
SylowC32 ⋊ C7×C19⋊AGL(1,𝔽5)
SylowC5 ⋊ C7×C3⋊Dic57

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(C3⋊(C19⋊AGL(1,𝔽5)))
commutator, hypocenterC32×C5×C19C4×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C19C4
prime radicalC32×C7×D5×C19C2
cosocleC32×D5×C19C2×C7
LCSG ▷ C32×C5×C19
UCSC1 ◁ C7

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5985

Conjugacy classes & character table

2415 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 727);