Finite Group Databasebeta

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C5×C11⋊#10587721 #44473295

order30030
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11⋊#10587721

Splittings

Fitting, socle, HallC5×C7×C11×C13 ⋊ C2×C3
derived, HallC7×C11×C13 ⋊ C2×C3×C5
HallC5×C11×#63271 ⋊ C2
HallC5×C13×D77 ⋊ C3
HallC11×#63271 ⋊ C2×C5
HallC13×D77 ⋊ C3×C5
HallC5×#63271 ⋊ D11
HallC5×D77 ⋊ C13⋊C3
HallC5×C11×C13 ⋊ AGL(1,𝔽7)
HallC5×C7×C13 ⋊ C3×D11
HallC5×C7×C11 ⋊ C2×C13⋊C3
Hall#63271 ⋊ C5×D11
HallD77 ⋊ C5×C13⋊C3
HallC11×C13 ⋊ C5×AGL(1,𝔽7)
HallC7×C13 ⋊ C3×C5×D11
HallC7×C11 ⋊ C2×C5×C13⋊C3
HallC5×C13 ⋊ C11⋊AGL(1,𝔽7)
HallC5×C11 ⋊ #10587721
HallC5×C7 ⋊ D11×C13⋊C3
SylowC13 ⋊ C5×C11⋊AGL(1,𝔽7)
SylowC11 ⋊ C5×#10587721
SylowC7 ⋊ C5×D11×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC5C11⋊#10587721
commutator, cosocle, hypocenterC7×C11×C13C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C11×C13C2×C3
LCSG ▷ C7×C11×C13
UCSC1 ◁ C5

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5005

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 80);