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C11×ΓL(1,𝔽8)×C47 #24925779

order10857
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C3×C11×C47 · Schur multiplier (H2) = C1

Aliases

direct productC11×ΓL(1,𝔽8)×C47
unambiguous semidirect productC7⋊(C3×C11×C47)
unambiguous semidirect product(C7×C11)⋊(C3×C47)
unambiguous semidirect product(C7×C47)⋊(C3×C11)
unambiguous semidirect product(C7×C11×C47)⋊C3

Splittings

Fitting, socle, HallC7×C11×C47 ⋊ C3
derived, SylowC7 ⋊ C3×C11×C47
HallC7×C47 ⋊ C3×C11
HallC7×C11 ⋊ C3×C47

Subgroups

subgroupG/H
center, hypercenterC11×C47ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C3×C11×C47
FrattiniC1G
Fitting, socleC7×C11×C47C3
LCSG ▷ C7
UCSC1 ◁ C11×C47

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2585 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C11×ΓL(1,𝔽8)×C47, C11×ΓL(1,𝔽8)×D47, ΓL(1,𝔽8)×D11×C47, …
maximal normal subgroup ofC2×C11×ΓL(1,𝔽8)×C47, C11×ΓL(1,𝔽8)×D47, ΓL(1,𝔽8)×D11×C47, …
maximal quotient ofC2×C11×ΓL(1,𝔽8)×C47, C11×C47×C7⋊C9, C3×C11×ΓL(1,𝔽8)×C47

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10857, 2);