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C13×ΓL(1,𝔽8)⋊D19 #23780595

order10374
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×ΓL(1,𝔽8)⋊D19
unambiguous semidirect productΓL(1,𝔽8)⋊(C13×D19)

Splittings

Fitting, socle, HallC7×C13×C19 ⋊ C2×C3
derived, HallC7×C19 ⋊ C2×C3×C13
HallC13×C19×ΓL(1,𝔽8) ⋊ C2
HallC13×D133 ⋊ C3
HallC19×ΓL(1,𝔽8) ⋊ C2×C13
HallC13×ΓL(1,𝔽8) ⋊ D19
HallD133 ⋊ C3×C13
HallC13×C19 ⋊ AGL(1,𝔽7)
HallC7×C13 ⋊ C3×D19
HallΓL(1,𝔽8) ⋊ C13×D19
SylowC19 ⋊ C13×AGL(1,𝔽7)
SylowC7 ⋊ C3×C13×D19

Subgroups

subgroupG/H
center, hypercenterC13ΓL(1,𝔽8)⋊D19
commutator, cosocle, hypocenterC7×C19C2×C3×C13
FrattiniC1G
Fitting, socleC7×C13×C19C2×C3
LCSG ▷ C7×C19
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

676 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13×D19×AGL(1,𝔽7), D13×ΓL(1,𝔽8)⋊D19, (ΓL(1,𝔽8)⋊D13)⋊D19, …
maximal normal subgroup ofC13×D19×AGL(1,𝔽7), D13×ΓL(1,𝔽8)⋊D19, (ΓL(1,𝔽8)⋊D13)⋊D19, …
maximal quotient ofC13×ΓL(1,𝔽8)⋊Dic19, C2×C13×ΓL(1,𝔽8)⋊D19, C13×(C7⋊C9)⋊D19, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10374, 86);