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C19×ΓL(1,𝔽8)⋊D13 #23780608

order10374
automorphism?
homologyAbelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×ΓL(1,𝔽8)⋊D13
unambiguous semidirect productΓL(1,𝔽8)⋊(C19×D13)

Splittings

Fitting, socle, HallC7×C13×C19 ⋊ C2×C3
derived, HallC7×C13 ⋊ C2×C3×C19
HallC13×C19×ΓL(1,𝔽8) ⋊ C2
HallC19×D91 ⋊ C3
HallC19×ΓL(1,𝔽8) ⋊ D13
HallC13×ΓL(1,𝔽8) ⋊ C2×C19
HallC13×C19 ⋊ AGL(1,𝔽7)
HallD91 ⋊ C3×C19
HallC7×C19 ⋊ C3×D13
HallΓL(1,𝔽8) ⋊ C19×D13
SylowC13 ⋊ C19×AGL(1,𝔽7)
SylowC7 ⋊ C3×C19×D13

Subgroups

subgroupG/H
center, hypercenterC19ΓL(1,𝔽8)⋊D13
commutator, cosocle, hypocenterC7×C13C2×C3×C19
FrattiniC1G
Fitting, socleC7×C13×C19C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C19

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC19×D13×AGL(1,𝔽7), (ΓL(1,𝔽8)⋊D13)⋊D19, D19×ΓL(1,𝔽8)⋊D13, …
maximal normal subgroup ofC19×D13×AGL(1,𝔽7), (ΓL(1,𝔽8)⋊D13)⋊D19, D19×ΓL(1,𝔽8)⋊D13, …
maximal quotient ofC19×ΓL(1,𝔽8)⋊Dic13, C2×C19×ΓL(1,𝔽8)⋊D13, C19×(C7⋊C9)⋊D13, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10374, 99);