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C3×C13×C7⋊AGL(1,𝔽11) #44473262

order30030
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×C7⋊AGL(1,𝔽11)
unambiguous semidirect product(C11⋊C5)⋊(C3×C13×D7)
unambiguous semidirect product(C3×D77)⋊(C5×C13)
unambiguous semidirect product(C3×C13×D77)⋊C5

Splittings

Fitting, socle, HallC3×C7×C11×C13 ⋊ C2×C5
derived, HallC7×C11 ⋊ C2×C3×C5×C13
HallC3×C7×C13×C11⋊C5 ⋊ C2
HallC3×C13×D77 ⋊ C5
HallC7×C13×C11⋊C5 ⋊ C2×C3
HallC3×C13×C11⋊C5 ⋊ D7
HallC13×D77 ⋊ C3×C5
HallC3×C7×C11⋊C5 ⋊ C2×C13
HallC7×C11×C13 ⋊ C2×C3×C5
HallC13×C11⋊C5 ⋊ C3×D7
HallC3×D77 ⋊ C5×C13
HallC3×C11×C13 ⋊ C5×D7
HallC7×C11⋊C5 ⋊ C2×C3×C13
HallC3×C7×C13 ⋊ AGL(1,𝔽11)
HallC3×C7×C11 ⋊ C2×C5×C13
HallC3×C11⋊C5 ⋊ C13×D7
HallD77 ⋊ C3×C5×C13
HallC11×C13 ⋊ C3×C5×D7
HallC7×C13 ⋊ C3×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C3×C13×D7
HallC3×C11 ⋊ C5×C13×D7
HallC3×C7 ⋊ C13×AGL(1,𝔽11)
SylowC11 ⋊ C3×C5×C13×D7
SylowC7 ⋊ C3×C13×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC3×C13C7⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC7×C11C2×C3×C5×C13
FrattiniC1G
Fitting, socleC3×C7×C11×C13C2×C5
LCSG ▷ C7×C11
UCSC1 ◁ C3×C13

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3003

Conjugacy classes & character table

1248 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 47);