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AGL(1,𝔽7)×D187 #30628109

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

Aliases

direct productAGL(1,𝔽7)×D187
unambiguous semidirect productD7⋊(C3×D187)
unambiguous semidirect product(C11×AGL(1,𝔽7))⋊D17
unambiguous semidirect product(C17×AGL(1,𝔽7))⋊D11
unambiguous semidirect product(D7×D187)⋊C3

Splittings

Fitting, socle, derived, HallC7×C11×C17 ⋊ C22×C3
HallD7×D187 ⋊ 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 ⋊ D11×AGL(1,𝔽7)
SylowC11 ⋊ D17×AGL(1,𝔽7)
SylowC7 ⋊ C2×C3×D187

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C17C22×C3
LCSG ▷ C7×C11×C17
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1309

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 30);