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C2×C11⋊(C17⋊AGL(1,𝔽7)) #30628119

order15708
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11⋊(C17⋊AGL(1,𝔽7))
unambiguous semidirect product(C2×C11)⋊(C17⋊AGL(1,𝔽7))
unambiguous semidirect product(C2×C17)⋊(C11⋊AGL(1,𝔽7))
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊D187
unambiguous semidirect product(C2×D1309)⋊C3

Splittings

Fitting, socleC2×C7×C11×C17 ⋊ C2×C3
derived, HallC7×C11×C17 ⋊ C22×C3
HallC2×D1309 ⋊ C3
HallC11×C17×ΓL(1,𝔽8) ⋊ C22
HallC17×ΓL(1,𝔽8) ⋊ C2×D11
HallC11×ΓL(1,𝔽8) ⋊ C2×D17
HallC11×C17 ⋊ C2×AGL(1,𝔽7)
HallC7×C17 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×C3×D17
HallΓL(1,𝔽8) ⋊ C2×D187
SylowC17 ⋊ C2×C11⋊AGL(1,𝔽7)
SylowC11 ⋊ C2×C17⋊AGL(1,𝔽7)
SylowC7 ⋊ C2×C3×D187

Subgroups

subgroupG/H
center, hypercenterC2C11⋊(C17⋊AGL(1,𝔽7))
commutator, cosocle, hypocenterC7×C11×C17C22×C3
FrattiniC1G
Fitting, socleC2×C7×C11×C17C2×C3
LCSG ▷ C7×C11×C17
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2618

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 40);