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C5×C13×C11⋊AGL(1,𝔽7) #44473293

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

Aliases

direct productC5×C13×C11⋊AGL(1,𝔽7)
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×C13×D11)
unambiguous semidirect product(C5×D77)⋊(C3×C13)

Splittings

Fitting, socle, HallC5×C7×C11×C13 ⋊ C2×C3
derived, HallC7×C11 ⋊ C2×C3×C5×C13
HallC5×C11×C13×ΓL(1,𝔽8) ⋊ C2
HallC5×C13×D77 ⋊ C3
HallC11×C13×ΓL(1,𝔽8) ⋊ C2×C5
HallC13×D77 ⋊ C3×C5
HallC5×C13×ΓL(1,𝔽8) ⋊ D11
HallC5×C11×ΓL(1,𝔽8) ⋊ C2×C13
HallC7×C11×C13 ⋊ C2×C3×C5
HallC5×D77 ⋊ C3×C13
HallC5×C11×C13 ⋊ AGL(1,𝔽7)
HallC5×C7×C13 ⋊ C3×D11
HallC5×C7×C11 ⋊ C2×C3×C13
HallC13×ΓL(1,𝔽8) ⋊ C5×D11
HallC11×ΓL(1,𝔽8) ⋊ C2×C5×C13
HallD77 ⋊ C3×C5×C13
HallC11×C13 ⋊ C5×AGL(1,𝔽7)
HallC5×ΓL(1,𝔽8) ⋊ C13×D11
HallC7×C13 ⋊ C3×C5×D11
HallC5×C11 ⋊ C13×AGL(1,𝔽7)
HallC5×C7 ⋊ C3×C13×D11
HallΓL(1,𝔽8) ⋊ C5×C13×D11
SylowC11 ⋊ C5×C13×AGL(1,𝔽7)
SylowC7 ⋊ C3×C5×C13×D11

Subgroups

subgroupG/H
center, hypercenterC5×C13C11⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC7×C11C2×C3×C5×C13
FrattiniC1G
Fitting, socleC5×C7×C11×C13C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C5×C13

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5005

Conjugacy classes & character table

2080 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 78);