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C19×ΓL(1,𝔽8)×D11 #22578624

order8778
automorphism?
homologyAbelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×ΓL(1,𝔽8)×D11
unambiguous semidirect productC11⋊(C2×C19×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D11)⋊(C3×C19)

Splittings

Fitting, socle, HallC7×C11×C19 ⋊ C2×C3
derived, HallC7×C11 ⋊ C2×C3×C19
HallC11×C19×ΓL(1,𝔽8) ⋊ C2
HallC7×C19×D11 ⋊ C3
HallC11×ΓL(1,𝔽8) ⋊ C2×C19
HallC11×C19 ⋊ C2×ΓL(1,𝔽8)
HallC7×D11 ⋊ C3×C19
HallC7×C19 ⋊ C3×D11
SylowC11 ⋊ C2×C19×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C19×D11

Subgroups

subgroupG/H
center, hypercenterC19ΓL(1,𝔽8)×D11
commutator, hypocenterC7×C11C2×C3×C19
FrattiniC1G
Fitting, socleC7×C11×C19C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C19

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

665 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC19×D11×AGL(1,𝔽7), D11×ΓL(1,𝔽8)⋊D19, ΓL(1,𝔽8)×D11×D19, …
maximal normal subgroup ofC19×D11×AGL(1,𝔽7), D11×ΓL(1,𝔽8)⋊D19, ΓL(1,𝔽8)×D11×D19, …
maximal quotient ofC19×ΓL(1,𝔽8)×Dic11, C2×C19×ΓL(1,𝔽8)×D11, C19×D11×C7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8778, 26);