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ΓL(1,𝔽8)×(C13⋊C3)⋊D19 #44527755

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

Aliases

direct productΓL(1,𝔽8)×(C13⋊C3)⋊D19
unambiguous semidirect product(C13⋊C3)⋊(ΓL(1,𝔽8)×D19)

Splittings

Fitting, socle, derived, HallC7×C13×C19 ⋊ C2×C32
HallC19×ΓL(1,𝔽8)×C13⋊C3 ⋊ C2
HallC7×D247 ⋊ C32
HallΓL(1,𝔽8)×C13⋊C3 ⋊ D19
HallD247 ⋊ C3×ΓL(1,𝔽8)
HallC13×C19 ⋊ C2×C3×ΓL(1,𝔽8)
HallC7×C19 ⋊ C3×D13⋊C3
HallC7×C13 ⋊ C32×D19
SylowC19 ⋊ ΓL(1,𝔽8)×D13⋊C3
SylowC13 ⋊ C3×ΓL(1,𝔽8)×D19
SylowC7 ⋊ C3×(C13⋊C3)⋊D19

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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 238);