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C2×C5×ΓL(1,𝔽8)×C19⋊C3 #26046152

order11970
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC2×C5×ΓL(1,𝔽8)×C19⋊C3
unambiguous semidirect product(C2×C7×C19⋊C3)⋊(C3×C5)
unambiguous semidirect product(C2×C19×ΓL(1,𝔽8))⋊(C3×C5)
unambiguous semidirect product(C2×#87704)⋊(C3×C5)
unambiguous semidirect product(C2×#87705)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C7×C19⋊C3)⋊C3
unambiguous semidirect product(C2×C5×C19×ΓL(1,𝔽8))⋊C3
unambiguous semidirect product(C2×C5×#87704)⋊C3
unambiguous semidirect product(C2×C5×#87705)⋊C3

Splittings

Fitting, socle, HallC2×C5×C7×C19 ⋊ C32
derived, HallC7×C19 ⋊ C2×C32×C5
HallC5×C7×C19 ⋊ C2×C32
HallC2×C7×C19 ⋊ C32×C5
HallC2×C5×C19 ⋊ C3×ΓL(1,𝔽8)
HallC5×C19 ⋊ C2×C3×ΓL(1,𝔽8)
HallC2×C5×C7 ⋊ C3×C19⋊C3
HallC2×C19 ⋊ C3×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C2×C3×C19⋊C3
SylowC19 ⋊ C2×C3×C5×ΓL(1,𝔽8)
HallC2×C7 ⋊ C3×C5×C19⋊C3
SylowC7 ⋊ C2×C3×C5×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5ΓL(1,𝔽8)×C19⋊C3
commutator, cosocle, hypocenterC7×C19C2×C32×C5
FrattiniC1G
Fitting, socleC2×C5×C7×C19C32
LCSG ▷ C7×C19
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

450 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×ΓL(1,𝔽8)⋊((C19⋊C3)⋊C4), C5×C19⋊C3×ΓL(1,𝔽8)⋊C4, C5×ΓL(1,𝔽8)×(C19⋊C3)⋊C4, …
maximal normal subgroup ofC5×ΓL(1,𝔽8)⋊((C19⋊C3)⋊C4), C5×C19⋊C3×ΓL(1,𝔽8)⋊C4, C5×ΓL(1,𝔽8)×(C19⋊C3)⋊C4, …
maximal quotient ofC4×C5×ΓL(1,𝔽8)×C19⋊C3, C22×C5×ΓL(1,𝔽8)×C19⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 81);