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C19×ΓL(1,𝔽8)⋊#261 #35208951

order20748
automorphism?
homologyAbelianization (H1) = C3×C4×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×ΓL(1,𝔽8)⋊#261
unambiguous semidirect productΓL(1,𝔽8)⋊(C19×#261)

Splittings

Fitting, socle, HallC7×C13×C19 ⋊ C3×C4
derived, HallC7×C13 ⋊ C3×C4×C19
HallC19×C7⋊#261 ⋊ C3
HallC13×C19×ΓL(1,𝔽8) ⋊ C4
HallC19×ΓL(1,𝔽8) ⋊ #261
HallC7⋊#261 ⋊ C3×C19
HallC13×ΓL(1,𝔽8) ⋊ C4×C19
HallC13×C19 ⋊ ΓL(1,𝔽8)⋊C4
HallC7×C19 ⋊ C3×#261
HallΓL(1,𝔽8) ⋊ C19×#261
SylowC13 ⋊ C19×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C3×C19×#261

Subgroups

subgroupG/H
center, hypercenterC19ΓL(1,𝔽8)⋊#261
commutator, hypocenterC7×C13C3×C4×C19
FrattiniC1G
Fitting, socleC7×C13×C19C3×C4
prime radicalC19×ΓL(1,𝔽8)×D13C2
cosocleC7×D13C2×C3×C19
LCSG ▷ C7×C13
UCSC1 ◁ C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1729

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20748, 179);