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C5×ΓL(1,𝔽8)×D143 #44473281

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

Aliases

direct productC5×ΓL(1,𝔽8)×D143

Splittings

Fitting, socle, HallC5×C7×C11×C13 ⋊ C2×C3
derived, HallC7×C11×C13 ⋊ C2×C3×C5
HallC5×C11×C13×ΓL(1,𝔽8) ⋊ C2
HallC5×C7×D143 ⋊ C3
HallC11×C13×ΓL(1,𝔽8) ⋊ C2×C5
HallC7×D143 ⋊ C3×C5
HallC5×C13×ΓL(1,𝔽8) ⋊ D11
HallC5×C11×ΓL(1,𝔽8) ⋊ D13
HallC5×C11×C13 ⋊ C2×ΓL(1,𝔽8)
HallC5×C7×C13 ⋊ C3×D11
HallC5×C7×C11 ⋊ C3×D13
HallC13×ΓL(1,𝔽8) ⋊ C5×D11
HallC11×ΓL(1,𝔽8) ⋊ C5×D13
HallC11×C13 ⋊ C2×C5×ΓL(1,𝔽8)
HallC7×C13 ⋊ C3×C5×D11
HallC7×C11 ⋊ C3×C5×D13
HallC5×C13 ⋊ ΓL(1,𝔽8)×D11
HallC5×C11 ⋊ ΓL(1,𝔽8)×D13
HallC5×C7 ⋊ C3×D143
SylowC13 ⋊ C5×ΓL(1,𝔽8)×D11
SylowC11 ⋊ C5×ΓL(1,𝔽8)×D13
SylowC7 ⋊ C3×C5×D143

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)×D143
commutator, cosocle, hypocenterC7×C11×C13C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C11×C13C2×C3
LCSG ▷ C7×C11×C13
UCSC1 ◁ C5

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5005

Conjugacy classes & character table

1825 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 66);