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C11×ΓL(1,𝔽8)×D35 #30633563

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

Aliases

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

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C2×C3
derived, HallC5×C72 ⋊ C2×C3×C11
HallC5×C7×C11×ΓL(1,𝔽8) ⋊ C2
HallC7×C11×D35 ⋊ C3
HallC7×C11×ΓL(1,𝔽8) ⋊ D5
HallC5×C7×ΓL(1,𝔽8) ⋊ C2×C11
HallC72×C11 ⋊ C3×D5
HallC7×D35 ⋊ C3×C11
HallC7×ΓL(1,𝔽8) ⋊ D5×C11
HallC5×C11 ⋊ D7×ΓL(1,𝔽8)
SylowC72 ⋊ C3×D5×C11
SylowC5 ⋊ C11×D7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC11ΓL(1,𝔽8)×D35
commutator, cosocle, hypocenterC5×C72C2×C3×C11
FrattiniC1G
Fitting, socleC5×C72×C11C2×C3
LCSG ▷ C5×C72
UCSC1 ◁ C11

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

1045 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×AGL(1,𝔽7)×D35, D35×C11⋊AGL(1,𝔽7), C11×(C5⋊AGL(1,𝔽7))⋊D7, …
maximal normal subgroup ofC11×AGL(1,𝔽7)×D35, D35×C11⋊AGL(1,𝔽7), C11×(C5⋊AGL(1,𝔽7))⋊D7, …
maximal quotient ofC11×ΓL(1,𝔽8)×Dic35, C2×C11×ΓL(1,𝔽8)×D35

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 108);