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C2×C5⋊(ΓL(1,𝔽8)⋊D47) #34089488

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

Aliases

direct productC2×C5⋊(ΓL(1,𝔽8)⋊D47)
unambiguous semidirect product(C2×C5)⋊(ΓL(1,𝔽8)⋊D47)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊D235
unambiguous semidirect product(C2×C47)⋊(C5⋊AGL(1,𝔽7))
unambiguous semidirect product(C2×D1645)⋊C3

Splittings

Fitting, socleC2×C5×C7×C47 ⋊ C2×C3
derived, HallC5×C7×C47 ⋊ C22×C3
HallC2×D1645 ⋊ C3
HallC5×ΓL(1,𝔽8)×C47 ⋊ C22
HallΓL(1,𝔽8)×C47 ⋊ C2×D5
HallC7×C47 ⋊ C2×C3×D5
HallC5×C47 ⋊ C2×AGL(1,𝔽7)
HallC5×ΓL(1,𝔽8) ⋊ C2×D47
SylowC47 ⋊ C2×C5⋊AGL(1,𝔽7)
HallC5×C7 ⋊ C2×C3×D47
HallΓL(1,𝔽8) ⋊ C2×D235
SylowC7 ⋊ C2×C3×D235
SylowC5 ⋊ C2×ΓL(1,𝔽8)⋊D47

Subgroups

subgroupG/H
center, hypercenterC2C5⋊(ΓL(1,𝔽8)⋊D47)
commutator, cosocle, hypocenterC5×C7×C47C22×C3
FrattiniC1G
Fitting, socleC2×C5×C7×C47C2×C3
LCSG ▷ C5×C7×C47
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3290

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19740, 41);