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ΓL(1,𝔽8)×#13093360 #44527764

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

Aliases

direct productΓL(1,𝔽8)×#13093360

Splittings

Fitting, socle, derived, HallC7×C13×C19 ⋊ C2×C32
HallΓL(1,𝔽8)×#10625202 ⋊ C2
HallC7×C13×D19 ⋊ C32
HallC13×D19 ⋊ C3×ΓL(1,𝔽8)
HallC7×D19 ⋊ C3×C13⋊C3
HallC13×C19 ⋊ C2×C3×ΓL(1,𝔽8)
HallC7×C19 ⋊ C2×C3×C13⋊C3
HallC7×C13 ⋊ C3×D19⋊C3
HallD19 ⋊ ΓL(1,𝔽8)×C13⋊C3
SylowC19 ⋊ C2×ΓL(1,𝔽8)×C13⋊C3
SylowC13 ⋊ ΓL(1,𝔽8)×D19⋊C3
SylowC7 ⋊ C3×#13093360

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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 247);