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C19×C5⋊(C5⋊AGL(1,𝔽7)) #34093041

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

Aliases

direct productC19×C5⋊(C5⋊AGL(1,𝔽7))
unambiguous semidirect productC5⋊(C19×C5⋊AGL(1,𝔽7))
unambiguous semidirect productΓL(1,𝔽8)⋊(C19×C5⋊D5)

Splittings

Fitting, socle, HallC52×C7×C19 ⋊ C2×C3
derived, HallC52×C7 ⋊ C2×C3×C19
HallC52×C19×ΓL(1,𝔽8) ⋊ C2
HallC19×C5⋊D35 ⋊ C3
HallC52×ΓL(1,𝔽8) ⋊ C2×C19
HallC52×C19 ⋊ AGL(1,𝔽7)
HallC19×ΓL(1,𝔽8) ⋊ C5⋊D5
HallC5⋊D35 ⋊ C3×C19
HallC7×C19 ⋊ C3×C5⋊D5
SylowC52 ⋊ C19×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C19×C5⋊D5
SylowC7 ⋊ C3×C19×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC19C5⋊(C5⋊AGL(1,𝔽7))
commutator, cosocle, hypocenterC52×C7C2×C3×C19
FrattiniC1G
Fitting, socleC52×C7×C19C2×C3
LCSG ▷ C52×C7
UCSC1 ◁ C19

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3325

Conjugacy classes & character table

1273 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19950, 80);