Finite Group Databasebeta

← Prev (#34089485) Next (#34089487) →

C2×C5×ΓL(1,𝔽8)×D47 #34089486

order19740
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×ΓL(1,𝔽8)×D47
unambiguous semidirect productC47⋊(C22×C5×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C47)⋊(C2×C5×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C7×D47)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C7×D47)⋊C3

Splittings

Fitting, socleC2×C5×C7×C47 ⋊ C2×C3
derived, HallC7×C47 ⋊ C22×C3×C5
HallC2×C5×C7×D47 ⋊ C3
HallC5×ΓL(1,𝔽8)×C47 ⋊ C22
HallC5×C7×C47 ⋊ C22×C3
HallC2×C7×D47 ⋊ C3×C5
HallΓL(1,𝔽8)×C47 ⋊ C22×C5
HallC5×C47 ⋊ C22×ΓL(1,𝔽8)
SylowC47 ⋊ C22×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C2×C3×D47
SylowC7 ⋊ C2×C3×C5×D47

Subgroups

subgroupG/H
center, hypercenterC2×C5ΓL(1,𝔽8)×D47
commutator, cosocle, hypocenterC7×C47C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C7×C47C2×C3
LCSG ▷ C7×C47
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3290

Conjugacy classes & character table

1250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19740, 39);