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C11×C5⋊#10587717 #44473307

order30030
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C5⋊#10587717
unambiguous semidirect productC5⋊(C11×#10587717)

Splittings

Fitting, socle, HallC5×C7×C11×C13 ⋊ C2×C3
derived, HallC5×C7×C13 ⋊ C2×C3×C11
HallC5×C11×#63271 ⋊ C2
HallC7×C11×D65 ⋊ C3
HallC11×#63271 ⋊ D5
HallC11×D65 ⋊ ΓL(1,𝔽8)
HallC5×#63271 ⋊ C2×C11
HallC7×C11×C13 ⋊ C3×D5
HallC7×D65 ⋊ C3×C11
HallC5×C11×C13 ⋊ C2×ΓL(1,𝔽8)
HallC5×C7×C11 ⋊ D13⋊C3
Hall#63271 ⋊ D5×C11
HallC11×C13 ⋊ D5×ΓL(1,𝔽8)
HallD65 ⋊ C11×ΓL(1,𝔽8)
HallC7×C13 ⋊ C3×D5×C11
HallC7×C11 ⋊ C5⋊(D13⋊C3)
HallC5×C13 ⋊ C2×C11×ΓL(1,𝔽8)
HallC5×C11 ⋊ #10587717
HallC5×C7 ⋊ C11×D13⋊C3
SylowC13 ⋊ D5×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C11×C5⋊(D13⋊C3)
SylowC5 ⋊ C11×#10587717

Subgroups

subgroupG/H
center, hypercenterC11C5⋊#10587717
commutator, cosocle, hypocenterC5×C7×C13C2×C3×C11
FrattiniC1G
Fitting, socleC5×C7×C11×C13C2×C3
LCSG ▷ C5×C7×C13
UCSC1 ◁ C11

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5005

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 92);