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C11×C17×C22⋊ΓL(1,𝔽8) #30628166

order15708
isoclinismisoclinic class of C22⋊ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C3×C11×C17 · Schur multiplier (H2) = C2

Aliases

direct productC11×C17×C22⋊ΓL(1,𝔽8)
unambiguous semidirect productC22⋊(C11×C17×ΓL(1,𝔽8))
unambiguous semidirect productC7⋊(C11×A4×C17)
unambiguous semidirect product(C22×C11)⋊(C17×ΓL(1,𝔽8))
unambiguous semidirect product(C22×C17)⋊(C11×ΓL(1,𝔽8))
unambiguous semidirect product(C7×C11)⋊(A4×C17)
unambiguous semidirect product(C7×C17)⋊(C11×A4)
unambiguous semidirect product(C22×C11×C17)⋊ΓL(1,𝔽8)
unambiguous semidirect product(C7×C11×C17)⋊A4

Splittings

Fitting, socle, HallC22×C7×C11×C17 ⋊ C3
derived, HallC22×C7 ⋊ C3×C11×C17
HallC7×C11×C17 ⋊ A4
HallC22×C11×C17 ⋊ ΓL(1,𝔽8)
HallC22×C7×C17 ⋊ C3×C11
HallC22×C7×C11 ⋊ C3×C17
HallC7×C17 ⋊ C11×A4
HallC7×C11 ⋊ A4×C17
HallC22×C17 ⋊ C11×ΓL(1,𝔽8)
HallC22×C11 ⋊ C17×ΓL(1,𝔽8)
SylowC7 ⋊ C11×A4×C17
SylowC22 ⋊ C11×C17×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC11×C17C22⋊ΓL(1,𝔽8)
commutator, cosocle, hypocenterC22×C7C3×C11×C17
FrattiniC1G
Fitting, socleC22×C7×C11×C17C3
LCSG ▷ C22×C7
UCSC1 ◁ C11×C17

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5236

Conjugacy classes & character table

2244 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 87);