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C19⋊C3×ΓL(1,𝔽8)⋊D13 #44527722

order31122
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC19⋊C3×ΓL(1,𝔽8)⋊D13
unambiguous semidirect productΓL(1,𝔽8)⋊(D13×C19⋊C3)

Splittings

Fitting, socle, derived, HallC7×C13×C19 ⋊ C2×C32
HallC13×ΓL(1,𝔽8)×C19⋊C3 ⋊ C2
HallC19×D91 ⋊ C32
HallΓL(1,𝔽8)×C19⋊C3 ⋊ D13
HallC13×C19 ⋊ C3×AGL(1,𝔽7)
HallD91 ⋊ C3×C19⋊C3
HallC7×C19 ⋊ C32×D13
HallC7×C13 ⋊ C2×C3×C19⋊C3
SylowC19 ⋊ C3×ΓL(1,𝔽8)⋊D13
SylowC13 ⋊ AGL(1,𝔽7)×C19⋊C3
SylowC7 ⋊ C3×D13×C19⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C13×C19C2×C32
LCSG ▷ C7×C13×C19
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1729

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 205);