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ΓL(1,𝔽8)×D11×C47 #36343979

order21714
automorphism?
homologyAbelianization (H1) = C2×C3×C47 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D11×C47
unambiguous semidirect productC11⋊(C2×ΓL(1,𝔽8)×C47)
unambiguous semidirect product(C7×D11)⋊(C3×C47)
unambiguous semidirect product(C7×D11×C47)⋊C3

Splittings

Fitting, socle, HallC7×C11×C47 ⋊ C2×C3
derived, HallC7×C11 ⋊ C2×C3×C47
HallC11×ΓL(1,𝔽8)×C47 ⋊ C2
HallC7×D11×C47 ⋊ C3
HallC11×C47 ⋊ C2×ΓL(1,𝔽8)
HallC7×C47 ⋊ C3×D11
HallC11×ΓL(1,𝔽8) ⋊ C2×C47
HallC7×D11 ⋊ C3×C47
SylowC11 ⋊ C2×ΓL(1,𝔽8)×C47
SylowC7 ⋊ C3×D11×C47

Subgroups

subgroupG/H
center, hypercenterC47ΓL(1,𝔽8)×D11
commutator, cosocle, hypocenterC7×C11C2×C3×C47
FrattiniC1G
Fitting, socleC7×C11×C47C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C47

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3619

Conjugacy classes & character table

1645 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21714, 19);