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D7×ΓL(1,𝔽8)×C11⋊C5 #30633509

order16170
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productD7×ΓL(1,𝔽8)×C11⋊C5
unambiguous semidirect product(C11×D7×ΓL(1,𝔽8))⋊C5

Splittings

Fitting, socle, derived, HallC72×C11 ⋊ C2×C3×C5
HallC7×ΓL(1,𝔽8)×C11⋊C5 ⋊ C2
HallC7×D7×C11⋊C5 ⋊ C3
HallC11×D7×ΓL(1,𝔽8) ⋊ C5
HallC72×C11⋊C5 ⋊ C2×C3
HallC7×C11×ΓL(1,𝔽8) ⋊ C2×C5
HallC7×C11×D7 ⋊ C3×C5
HallC7×ΓL(1,𝔽8) ⋊ C2×C11⋊C5
HallC7×D7 ⋊ C3×C11⋊C5
SylowC72 ⋊ C2×C3×C11⋊C5
SylowC11 ⋊ C5×D7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC72×C11C2×C3×C5
LCSG ▷ C72×C11
UCSC1

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 462

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD7×ΓL(1,𝔽8)⋊AGL(1,𝔽11), D7×AGL(1,𝔽7)×C11⋊C5, D7×ΓL(1,𝔽8)×AGL(1,𝔽11), …
maximal normal subgroup ofD7×ΓL(1,𝔽8)⋊AGL(1,𝔽11), D7×AGL(1,𝔽7)×C11⋊C5, D7×ΓL(1,𝔽8)×AGL(1,𝔽11), …
maximal quotient ofΓL(1,𝔽8)×Dic7×C11⋊C5, C2×D7×ΓL(1,𝔽8)×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 54);