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C2×C19×ΓL(1,𝔽8)2 #30660741

order16758
automorphism?
homologyAbelianization (H1) = C2×C32×C19 · Schur multiplier (H2) = C3

Aliases

direct productC2×C19×ΓL(1,𝔽8)2
unambiguous semidirect product(C2×C7×ΓL(1,𝔽8))⋊(C3×C19)
unambiguous semidirect product(C2×#3861)⋊(C3×C19)
unambiguous semidirect product(C2×#3862)⋊(C3×C19)

Splittings

Fitting, socle, HallC2×C72×C19 ⋊ C32
derived, SylowC72 ⋊ C2×C32×C19
HallC72×C19 ⋊ C2×C32
HallC2×C72 ⋊ C32×C19

Subgroups

subgroupG/H
center, hypercenterC2×C19ΓL(1,𝔽8)2
commutator, cosocle, hypocenterC72C2×C32×C19
FrattiniC1G
Fitting, socleC2×C72×C19C32
LCSG ▷ C72
UCSC1 ◁ C2×C19

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 798

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC19×ΓL(1,𝔽8)⋊(ΓL(1,𝔽8)⋊C4), ΓL(1,𝔽8)⋊(ΓL(1,𝔽8)⋊Dic19), C19×ΓL(1,𝔽8)×ΓL(1,𝔽8)⋊C4, …
maximal normal subgroup ofC19×ΓL(1,𝔽8)⋊(ΓL(1,𝔽8)⋊C4), ΓL(1,𝔽8)⋊(ΓL(1,𝔽8)⋊Dic19), C19×ΓL(1,𝔽8)×ΓL(1,𝔽8)⋊C4, …
maximal quotient ofC4×C19×ΓL(1,𝔽8)2, C22×C19×ΓL(1,𝔽8)2

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16758, 268);