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C5×C11×#10620252 #49088979

order35805
automorphism?
homologyAbelianization (H1) = C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×#10620252

Splittings

Fitting, socle, HallC5×C7×C11×C31 ⋊ C3
derived, HallC7×C31 ⋊ C3×C5×C11
HallC7×C11×C31 ⋊ C3×C5
HallC5×C11×C31 ⋊ ΓL(1,𝔽8)
HallC5×C7×C31 ⋊ C3×C11
HallC5×C7×C11 ⋊ C31⋊C3
HallC11×C31 ⋊ C5×ΓL(1,𝔽8)
HallC5×C31 ⋊ C11×ΓL(1,𝔽8)
HallC7×C11 ⋊ C5×C31⋊C3
HallC5×C7 ⋊ C11×C31⋊C3
SylowC31 ⋊ C5×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C5×C11×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC5×C11#10620252
commutator, cosocle, hypocenterC7×C31C3×C5×C11
FrattiniC1G
Fitting, socleC5×C7×C11×C31C3
LCSG ▷ C7×C31
UCSC1 ◁ C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11935

Conjugacy classes & character table

4125 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35805, 11);