Finite Group Databasebeta

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C5×C11×C13×AGL(1,𝔽7) #44473285

order30030
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×C13×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×C5×C11×C13)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C5×C11×C13)
unambiguous semidirect product(C5×D7)⋊(C3×C11×C13)
unambiguous semidirect product(C5×C11×D7)⋊(C3×C13)

Splittings

Fitting, socle, HallC5×C7×C11×C13 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C3×C5×C11×C13
HallC5×C11×C13×ΓL(1,𝔽8) ⋊ C2
HallC5×C11×C13×D7 ⋊ C3
HallC11×C13×ΓL(1,𝔽8) ⋊ C2×C5
HallC11×C13×D7 ⋊ C3×C5
HallC5×C13×ΓL(1,𝔽8) ⋊ C2×C11
HallC5×C11×ΓL(1,𝔽8) ⋊ C2×C13
HallC7×C11×C13 ⋊ C2×C3×C5
HallC5×C13×D7 ⋊ C3×C11
HallC5×C11×D7 ⋊ C3×C13
HallC5×C7×C13 ⋊ C2×C3×C11
HallC5×C7×C11 ⋊ C2×C3×C13
HallC13×ΓL(1,𝔽8) ⋊ C2×C5×C11
HallC11×ΓL(1,𝔽8) ⋊ C2×C5×C13
HallC13×D7 ⋊ C3×C5×C11
HallC11×D7 ⋊ C3×C5×C13
HallC5×ΓL(1,𝔽8) ⋊ C2×C11×C13
HallC7×C13 ⋊ C2×C3×C5×C11
HallC7×C11 ⋊ C2×C3×C5×C13
HallC5×D7 ⋊ C3×C11×C13
HallC5×C7 ⋊ C2×C3×C11×C13
HallΓL(1,𝔽8) ⋊ C2×C5×C11×C13
HallD7 ⋊ C3×C5×C11×C13

Subgroups

subgroupG/H
center, hypercenterC5×C11×C13AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C2×C3×C5×C11×C13
FrattiniC1G
Fitting, socleC5×C7×C11×C13C2×C3
LCSG ▷ C7
UCSC1 ◁ C5×C11×C13

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5005

Conjugacy classes & character table

5005 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 70);