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C11×C5⋊(ΓL(1,𝔽8)⋊D7) #30633557

order16170
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C5⋊(ΓL(1,𝔽8)⋊D7)
unambiguous semidirect productC5⋊(C11×ΓL(1,𝔽8)⋊D7)
unambiguous semidirect productΓL(1,𝔽8)⋊(C11×D35)

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C2×C3
derived, HallC5×C72 ⋊ C2×C3×C11
HallC5×C7×C11×ΓL(1,𝔽8) ⋊ C2
HallC11×C5⋊(C7⋊D7) ⋊ C3
HallC7×C11×ΓL(1,𝔽8) ⋊ D5
HallC5×C7×ΓL(1,𝔽8) ⋊ C2×C11
HallC72×C11 ⋊ C3×D5
HallC5⋊(C7⋊D7) ⋊ C3×C11
HallC7×ΓL(1,𝔽8) ⋊ D5×C11
HallC5×C11 ⋊ ΓL(1,𝔽8)⋊D7
SylowC72 ⋊ C3×D5×C11
SylowC5 ⋊ C11×ΓL(1,𝔽8)⋊D7

Subgroups

subgroupG/H
center, hypercenterC11C5⋊(ΓL(1,𝔽8)⋊D7)
commutator, cosocle, hypocenterC5×C72C2×C3×C11
FrattiniC1G
Fitting, socleC5×C72×C11C2×C3
LCSG ▷ C5×C72
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1155

Conjugacy classes & character table

1012 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD11×C5⋊(ΓL(1,𝔽8)⋊D7), D5×C11×ΓL(1,𝔽8)⋊D7, D55⋊(ΓL(1,𝔽8)⋊D7), …
maximal normal subgroup ofD11×C5⋊(ΓL(1,𝔽8)⋊D7), D5×C11×ΓL(1,𝔽8)⋊D7, D55⋊(ΓL(1,𝔽8)⋊D7), …
maximal quotient ofC11×ΓL(1,𝔽8)⋊Dic35, C2×C11×C5⋊(ΓL(1,𝔽8)⋊D7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 102);