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C3×C11×C17⋊AGL(1,𝔽7) #37555633

order23562
automorphism?
homologyAbelianization (H1) = C2×C32×C11 · Schur multiplier (H2) = C3

Aliases

direct productC3×C11×C17⋊AGL(1,𝔽7)
unambiguous semidirect productC17⋊(C3×C11×AGL(1,𝔽7))
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×C11×D17)
unambiguous semidirect productD119⋊(C32×C11)
unambiguous semidirect product(C3×D119)⋊(C3×C11)
unambiguous semidirect product(C11×D119)⋊C32
unambiguous semidirect product(C3×C11×D119)⋊C3

Splittings

Fitting, socleC3×C7×C11×C17 ⋊ C2×C3
derived, HallC7×C17 ⋊ C2×C32×C11
HallC3×C11×C17×ΓL(1,𝔽8) ⋊ C2
HallC11×D119 ⋊ C32
HallC7×C11×C17 ⋊ C2×C32
HallC3×C17×ΓL(1,𝔽8) ⋊ C2×C11
HallC3×C11×ΓL(1,𝔽8) ⋊ D17
HallD119 ⋊ C32×C11
HallC11×C17 ⋊ C3×AGL(1,𝔽7)
HallC7×C11 ⋊ C32×D17
HallC3×ΓL(1,𝔽8) ⋊ C11×D17
SylowC17 ⋊ C3×C11×AGL(1,𝔽7)
SylowC7 ⋊ C32×C11×D17

Subgroups

subgroupG/H
center, hypercenterC3×C11C17⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC7×C17C2×C32×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C17C2×C3
LCSG ▷ C7×C17
UCSC1 ◁ C3×C11

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3927

Conjugacy classes & character table

1551 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 27);