Finite Group Databasebeta

← Prev (#21463263) Next (#21463265) →

C2×C11×C17×ΓL(1,𝔽8) #21463264

order7854
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC2×C11×C17×ΓL(1,𝔽8)
unambiguous semidirect product(C2×C7)⋊(C3×C11×C17)
unambiguous semidirect product(C2×C7×C11)⋊(C3×C17)
unambiguous semidirect product(C2×C7×C17)⋊(C3×C11)
unambiguous semidirect product(C2×C7×C11×C17)⋊C3

Splittings

Fitting, socle, HallC2×C7×C11×C17 ⋊ C3
derived, SylowC7 ⋊ C2×C3×C11×C17
HallC7×C11×C17 ⋊ C2×C3
HallC2×C7×C17 ⋊ C3×C11
HallC2×C7×C11 ⋊ C3×C17
HallC7×C17 ⋊ C2×C3×C11
HallC7×C11 ⋊ C2×C3×C17
HallC2×C7 ⋊ C3×C11×C17

Subgroups

subgroupG/H
center, hypercenterC2×C11×C17ΓL(1,𝔽8)
commutator, hypocenterC7C2×C3×C11×C17
FrattiniC1G
Fitting, socleC2×C7×C11×C17C3
LCSG ▷ C7
UCSC1 ◁ C2×C11×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1870 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C11×C17×ΓL(1,𝔽8), C11×ΓL(1,𝔽8)×Dic17, C17×ΓL(1,𝔽8)×Dic11, …
maximal normal subgroup ofC4×C11×C17×ΓL(1,𝔽8), C11×ΓL(1,𝔽8)×Dic17, C17×ΓL(1,𝔽8)×Dic11, …
maximal quotient ofC4×C11×C17×ΓL(1,𝔽8), C22×C11×C17×ΓL(1,𝔽8), C2×C11×C17×C7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7854, 2);