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C19×(C5⋊D5)⋊ΓL(1,𝔽8) #34093069

order19950
automorphism?
homologyAbelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C5

Aliases

direct productC19×(C5⋊D5)⋊ΓL(1,𝔽8)
unambiguous semidirect product(C5⋊D5)⋊(C19×ΓL(1,𝔽8))

Splittings

Fitting, socle, HallC52×C7×C19 ⋊ C2×C3
derived, HallC52×C7 ⋊ C2×C3×C19
HallC19×C7⋊(C52⋊C3) ⋊ C2
HallC7×C19×C5⋊D5 ⋊ C3
HallC19×C5⋊D5 ⋊ ΓL(1,𝔽8)
HallC7⋊(C52⋊C3) ⋊ C2×C19
HallC52×C19 ⋊ C2×ΓL(1,𝔽8)
HallC7×C5⋊D5 ⋊ C3×C19
HallC7×C19 ⋊ (C5⋊D5)⋊C3
HallC5⋊D5 ⋊ C19×ΓL(1,𝔽8)
SylowC52 ⋊ C2×C19×ΓL(1,𝔽8)
SylowC7 ⋊ C19×(C5⋊D5)⋊C3

Subgroups

subgroupG/H
center, hypercenterC19(C5⋊D5)⋊ΓL(1,𝔽8)
commutator, cosocle, hypocenterC52×C7C2×C3×C19
FrattiniC1G
Fitting, socleC52×C7×C19C2×C3
LCSG ▷ C52×C7
UCSC1 ◁ C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1995

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19950, 108);