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C11×ΓL(1,𝔽8)×C52⋊C3 #31773157

order17325
automorphism?
homologyAbelianization (H1) = C32×C11 · Schur multiplier (H2) = C3×C5

Aliases

direct productC11×ΓL(1,𝔽8)×C52⋊C3
unambiguous semidirect product(C52×ΓL(1,𝔽8))⋊(C3×C11)
unambiguous semidirect product(C7×C52⋊C3)⋊(C3×C11)
unambiguous semidirect product(C7⋊(C52⋊C3))⋊(C3×C11)
unambiguous semidirect product(C52×C11×ΓL(1,𝔽8))⋊C3
unambiguous semidirect product(C7×C11×C52⋊C3)⋊C3
unambiguous semidirect product(C11×C7⋊(C52⋊C3))⋊C3

Splittings

Fitting, socle, HallC52×C7×C11 ⋊ C32
derived, HallC52×C7 ⋊ C32×C11
HallC52×C11 ⋊ C3×ΓL(1,𝔽8)
HallC7×C11 ⋊ C3×C52⋊C3
SylowC52 ⋊ C3×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C11×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC11ΓL(1,𝔽8)×C52⋊C3
commutator, cosocle, hypocenterC52×C7C32×C11
FrattiniC1G
Fitting, socleC52×C7×C11C32
LCSG ▷ C52×C7
UCSC1 ◁ C11

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1155

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC11×AGL(1,𝔽7)×C52⋊C3, C52⋊C3×C11⋊AGL(1,𝔽7), ΓL(1,𝔽8)×D11×C52⋊C3, …
maximal normal subgroup ofC11×AGL(1,𝔽7)×C52⋊C3, C52⋊C3×C11⋊AGL(1,𝔽7), ΓL(1,𝔽8)×D11×C52⋊C3, …
maximal quotient ofC2×C11×ΓL(1,𝔽8)×C52⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17325, 17);