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C5×C11×ΓL(1,𝔽8)⋊D13 #44473289

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

Aliases

direct productC5×C11×ΓL(1,𝔽8)⋊D13
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×C11×D13)

Splittings

Fitting, socle, HallC5×C7×C11×C13 ⋊ C2×C3
derived, HallC7×C13 ⋊ C2×C3×C5×C11
HallC5×C11×C13×ΓL(1,𝔽8) ⋊ C2
HallC5×C11×D91 ⋊ C3
HallC11×C13×ΓL(1,𝔽8) ⋊ C2×C5
HallC11×D91 ⋊ C3×C5
HallC5×C13×ΓL(1,𝔽8) ⋊ C2×C11
HallC5×C11×ΓL(1,𝔽8) ⋊ D13
HallC7×C11×C13 ⋊ C2×C3×C5
HallC5×D91 ⋊ C3×C11
HallC5×C11×C13 ⋊ AGL(1,𝔽7)
HallC5×C7×C13 ⋊ C2×C3×C11
HallC5×C7×C11 ⋊ C3×D13
HallC13×ΓL(1,𝔽8) ⋊ C2×C5×C11
HallC11×ΓL(1,𝔽8) ⋊ C5×D13
HallD91 ⋊ C3×C5×C11
HallC11×C13 ⋊ C5×AGL(1,𝔽7)
HallC5×ΓL(1,𝔽8) ⋊ C11×D13
HallC7×C11 ⋊ C3×C5×D13
HallC5×C13 ⋊ C11×AGL(1,𝔽7)
HallC5×C7 ⋊ C3×C11×D13
HallΓL(1,𝔽8) ⋊ C5×C11×D13
SylowC13 ⋊ C5×C11×AGL(1,𝔽7)
SylowC7 ⋊ C3×C5×C11×D13

Subgroups

subgroupG/H
center, hypercenterC5×C11ΓL(1,𝔽8)⋊D13
commutator, cosocle, hypocenterC7×C13C2×C3×C5×C11
FrattiniC1G
Fitting, socleC5×C7×C11×C13C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C5×C11

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5005

Conjugacy classes & character table

2035 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 74);