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C11⋊C5×#10620253 #49088993

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

Aliases

direct productC11⋊C5×#10620253
unambiguous semidirect productC11⋊(C5×#10620253)

Splittings

Fitting, socle, derived, HallC7×C11×C31 ⋊ C3×C5
HallC7×C31×C11⋊C5 ⋊ C3
HallC11×#10620253 ⋊ C5
HallC31×C11⋊C5 ⋊ ΓL(1,𝔽8)
HallC7×C11⋊C5 ⋊ C31⋊C3
HallC11×C31 ⋊ C5×ΓL(1,𝔽8)
HallC7×C31 ⋊ C3×C11⋊C5
HallC7×C11 ⋊ C5×C31⋊C3
SylowC31 ⋊ ΓL(1,𝔽8)×C11⋊C5
SylowC11 ⋊ C5×#10620253
SylowC7 ⋊ C11⋊C5×C31⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C31C3×C5
LCSG ▷ C7×C11×C31
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2387

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35805, 25);