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C23×C37×AGL(1,𝔽7) #49088371

order35742
automorphism?
homologyAbelianization (H1) = C2×C3×C23×C37 · Schur multiplier (H2) = C1

Aliases

direct productC23×C37×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×C23×C37)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C23×C37)
unambiguous semidirect product(D7×C23)⋊(C3×C37)

Splittings

Fitting, socle, HallC7×C23×C37 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C3×C23×C37
HallΓL(1,𝔽8)×C23×C37 ⋊ C2
HallD7×C23×C37 ⋊ C3
HallΓL(1,𝔽8)×C37 ⋊ C2×C23
HallD7×C37 ⋊ C3×C23
HallΓL(1,𝔽8)×C23 ⋊ C2×C37
HallD7×C23 ⋊ C3×C37
HallC7×C37 ⋊ C2×C3×C23
HallC7×C23 ⋊ C2×C3×C37
HallΓL(1,𝔽8) ⋊ C2×C23×C37
HallD7 ⋊ C3×C23×C37

Subgroups

subgroupG/H
center, hypercenterC23×C37AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C2×C3×C23×C37
FrattiniC1G
Fitting, socleC7×C23×C37C2×C3
LCSG ▷ C7
UCSC1 ◁ C23×C37

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5957

Conjugacy classes & character table

5957 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35742, 34);