Finite Group Databasebeta

← Prev (#44527774) Next (#44527776) →

ΓL(1,𝔽8)×(C19⋊C3)⋊D13 #44527775

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

Aliases

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

Splittings

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

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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 258);