Finite Group Databasebeta

← Prev (#34093029) Next (#34093031) →

C5×C5⋊(ΓL(1,𝔽8)⋊D19) #34093030

order19950
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C5⋊(ΓL(1,𝔽8)⋊D19)
unambiguous semidirect productC5⋊(C5×ΓL(1,𝔽8)⋊D19)
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×D95)

Splittings

Fitting, socle, HallC52×C7×C19 ⋊ C2×C3
derivedC5×C7×C19 ⋊ C2×C3×C5
HallC52×C19×ΓL(1,𝔽8) ⋊ C2
HallC5×D665 ⋊ C3
HallC52×ΓL(1,𝔽8) ⋊ D19
HallC52×C19 ⋊ AGL(1,𝔽7)
HallC19×ΓL(1,𝔽8) ⋊ C5×D5
HallC52×C7 ⋊ C3×D19
HallC7×C19 ⋊ C3×C5×D5
SylowC52 ⋊ ΓL(1,𝔽8)⋊D19
HallΓL(1,𝔽8) ⋊ C5×D95
SylowC19 ⋊ C5×C5⋊AGL(1,𝔽7)
SylowC7 ⋊ C3×C5×D95

Subgroups

subgroupG/H
center, hypercenterC5C5⋊(ΓL(1,𝔽8)⋊D19)
commutator, cosocle, hypocenterC5×C7×C19C2×C3×C5
FrattiniC1G
Fitting, socleC52×C7×C19C2×C3
LCSG ▷ C5×C7×C19
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1330

Conjugacy classes & character table

1210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19950, 69);