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C11×ΓL(1,𝔽8)⋊D19 #22578636

order8778
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×ΓL(1,𝔽8)⋊D19
unambiguous semidirect productΓL(1,𝔽8)⋊(C11×D19)

Splittings

Fitting, socle, HallC7×C11×C19 ⋊ C2×C3
derived, HallC7×C19 ⋊ C2×C3×C11
HallC11×C19×ΓL(1,𝔽8) ⋊ C2
HallC11×D133 ⋊ C3
HallC19×ΓL(1,𝔽8) ⋊ C2×C11
HallD133 ⋊ C3×C11
HallC11×ΓL(1,𝔽8) ⋊ D19
HallC11×C19 ⋊ AGL(1,𝔽7)
HallC7×C11 ⋊ C3×D19
HallΓL(1,𝔽8) ⋊ C11×D19
SylowC19 ⋊ C11×AGL(1,𝔽7)
SylowC7 ⋊ C3×C11×D19

Subgroups

subgroupG/H
center, hypercenterC11ΓL(1,𝔽8)⋊D19
commutator, hypocenterC7×C19C2×C3×C11
FrattiniC1G
Fitting, socleC7×C11×C19C2×C3
LCSG ▷ C7×C19
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×D19×AGL(1,𝔽7), D11×ΓL(1,𝔽8)⋊D19, (C11⋊AGL(1,𝔽7))⋊D19, …
maximal normal subgroup ofC11×D19×AGL(1,𝔽7), D11×ΓL(1,𝔽8)⋊D19, (C11⋊AGL(1,𝔽7))⋊D19, …
maximal quotient ofC11×ΓL(1,𝔽8)⋊Dic19, C2×C11×ΓL(1,𝔽8)⋊D19, C11×(C7⋊C9)⋊D19, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8778, 38);