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D5×C11×C13×ΓL(1,𝔽8) #44473301

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

Aliases

direct productD5×C11×C13×ΓL(1,𝔽8)
unambiguous semidirect productC5⋊(C2×C11×C13×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D5)⋊(C3×C11×C13)
unambiguous semidirect product(C7×D5×C11)⋊(C3×C13)

Splittings

Fitting, socle, HallC5×C7×C11×C13 ⋊ C2×C3
derived, HallC5×C7 ⋊ C2×C3×C11×C13
HallC5×C11×C13×ΓL(1,𝔽8) ⋊ C2
HallC7×D5×C11×C13 ⋊ C3
HallC5×C13×ΓL(1,𝔽8) ⋊ C2×C11
HallC5×C11×ΓL(1,𝔽8) ⋊ C2×C13
HallC7×C11×C13 ⋊ C3×D5
HallC7×D5×C13 ⋊ C3×C11
HallC7×D5×C11 ⋊ C3×C13
HallC5×C11×C13 ⋊ C2×ΓL(1,𝔽8)
HallC5×C7×C13 ⋊ C2×C3×C11
HallC5×C7×C11 ⋊ C2×C3×C13
HallC5×ΓL(1,𝔽8) ⋊ C2×C11×C13
HallC7×C13 ⋊ C3×D5×C11
HallC7×C11 ⋊ C3×D5×C13
HallC7×D5 ⋊ C3×C11×C13
HallC5×C13 ⋊ C2×C11×ΓL(1,𝔽8)
HallC5×C11 ⋊ C2×C13×ΓL(1,𝔽8)
SylowC7 ⋊ C3×D5×C11×C13
SylowC5 ⋊ C2×C11×C13×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC11×C13D5×ΓL(1,𝔽8)
commutator, cosocle, hypocenterC5×C7C2×C3×C11×C13
FrattiniC1G
Fitting, socleC5×C7×C11×C13C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C11×C13

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5005

Conjugacy classes & character table

2860 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 86);