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C7×C11×ΓL(1,𝔽32) #26045641

order11935
isoclinismisoclinic class of ΓL(1,𝔽32)
automorphism?
homologyAbelianization (H1) = C5×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×ΓL(1,𝔽32)
unambiguous semidirect productC31⋊(C5×C7×C11)
unambiguous semidirect product(C7×C31)⋊(C5×C11)

Splittings

Fitting, socle, HallC7×C11×C31 ⋊ C5
derived, SylowC31 ⋊ C5×C7×C11
HallC11×C31 ⋊ C5×C7
HallC7×C31 ⋊ C5×C11

Subgroups

subgroupG/H
center, hypercenterC7×C11ΓL(1,𝔽32)
commutator, cosocle, hypocenterC31C5×C7×C11
FrattiniC1G
Fitting, socleC7×C11×C31C5
LCSG ▷ C31
UCSC1 ◁ C7×C11

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

847 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C7×C11×ΓL(1,𝔽32), C7×C11×D31⋊C5, C7×D11×ΓL(1,𝔽32), …
maximal normal subgroup ofC2×C7×C11×ΓL(1,𝔽32), C7×C11×D31⋊C5, C7×D11×ΓL(1,𝔽32), …
maximal quotient ofC2×C7×C11×ΓL(1,𝔽32), C3×C7×C11×ΓL(1,𝔽32)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11935, 2);