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C2×C11×C17×AGL(1,𝔽7) #30628116

order15708
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C22×C3×C11×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×C17×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C2×C3×C11×C17)
unambiguous semidirect productΓL(1,𝔽8)⋊(C22×C11×C17)
unambiguous semidirect product(C2×D7)⋊(C3×C11×C17)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C2×C11×C17)
unambiguous semidirect product(C2×C11×D7)⋊(C3×C17)
unambiguous semidirect product(C2×D7×C17)⋊(C3×C11)
unambiguous semidirect product(C2×C11×D7×C17)⋊C3

Splittings

Fitting, socleC2×C7×C11×C17 ⋊ C2×C3
derived, SylowC7 ⋊ C22×C3×C11×C17
HallC2×C11×D7×C17 ⋊ C3
HallC11×C17×ΓL(1,𝔽8) ⋊ C22
HallC7×C11×C17 ⋊ C22×C3
HallC2×D7×C17 ⋊ C3×C11
HallC17×ΓL(1,𝔽8) ⋊ C22×C11
HallC2×C11×D7 ⋊ C3×C17
HallC11×ΓL(1,𝔽8) ⋊ C22×C17
HallC7×C17 ⋊ C22×C3×C11
HallC7×C11 ⋊ C22×C3×C17
HallC2×D7 ⋊ C3×C11×C17
HallΓL(1,𝔽8) ⋊ C22×C11×C17

Subgroups

subgroupG/H
center, hypercenterC2×C11×C17AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C22×C3×C11×C17
FrattiniC1G
Fitting, socleC2×C7×C11×C17C2×C3
LCSG ▷ C7
UCSC1 ◁ C2×C11×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2618

Conjugacy classes & character table

2618 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 37);