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C113×C5⋊AGL(1,𝔽7) #37557555

order23730
automorphism?
homologyAbelianization (H1) = C2×C3×C113 · Schur multiplier (H2) = C1

Aliases

direct productC113×C5⋊AGL(1,𝔽7)
unambiguous semidirect productC5⋊(AGL(1,𝔽7)×C113)
unambiguous semidirect productΓL(1,𝔽8)⋊(D5×C113)
unambiguous semidirect productD35⋊(C3×C113)
unambiguous semidirect product(D35×C113)⋊C3

Splittings

Fitting, socle, HallC5×C7×C113 ⋊ C2×C3
derived, HallC5×C7 ⋊ C2×C3×C113
HallC5×ΓL(1,𝔽8)×C113 ⋊ C2
HallD35×C113 ⋊ C3
HallΓL(1,𝔽8)×C113 ⋊ D5
HallC7×C113 ⋊ C3×D5
HallC5×C113 ⋊ AGL(1,𝔽7)
HallC5×ΓL(1,𝔽8) ⋊ C2×C113
HallD35 ⋊ C3×C113
HallΓL(1,𝔽8) ⋊ D5×C113
SylowC7 ⋊ C3×D5×C113
SylowC5 ⋊ AGL(1,𝔽7)×C113

Subgroups

subgroupG/H
center, hypercenterC113C5⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC5×C7C2×C3×C113
FrattiniC1G
Fitting, socleC5×C7×C113C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C113

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3955

Conjugacy classes & character table

1921 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23730, 31);