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C31×C17⋊AGL(1,𝔽7) #36349017

order22134
automorphism?
homologyAbelianization (H1) = C2×C3×C31 · Schur multiplier (H2) = C1

Aliases

direct productC31×C17⋊AGL(1,𝔽7)
unambiguous semidirect productC17⋊(C31×AGL(1,𝔽7))
unambiguous semidirect productΓL(1,𝔽8)⋊(C31×D17)
unambiguous semidirect productD119⋊(C3×C31)

Splittings

Fitting, socle, HallC7×C17×C31 ⋊ C2×C3
derived, HallC7×C17 ⋊ C2×C3×C31
HallC17×ΓL(1,𝔽8)×C31 ⋊ C2
HallC31×D119 ⋊ C3
HallΓL(1,𝔽8)×C31 ⋊ D17
HallC17×C31 ⋊ AGL(1,𝔽7)
HallC17×ΓL(1,𝔽8) ⋊ C2×C31
HallD119 ⋊ C3×C31
HallC7×C31 ⋊ C3×D17
HallΓL(1,𝔽8) ⋊ C31×D17
SylowC17 ⋊ C31×AGL(1,𝔽7)
SylowC7 ⋊ C3×C31×D17

Subgroups

subgroupG/H
center, hypercenterC31C17⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC7×C17C2×C3×C31
FrattiniC1G
Fitting, socleC7×C17×C31C2×C3
LCSG ▷ C7×C17
UCSC1 ◁ C31

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3689

Conjugacy classes & character table

1457 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22134, 42);