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C5×C47×C22⋊ΓL(1,𝔽8) #34089534

order19740
automorphism?
homologyAbelianization (H1) = C3×C5×C47 · Schur multiplier (H2) = C2

Aliases

direct productC5×C47×C22⋊ΓL(1,𝔽8)
unambiguous semidirect productC22⋊(C5×ΓL(1,𝔽8)×C47)
unambiguous semidirect productC7⋊(C5×A4×C47)
unambiguous semidirect product(C22×C5)⋊(ΓL(1,𝔽8)×C47)
unambiguous semidirect product(C5×C7)⋊(A4×C47)
unambiguous semidirect product(C22×C47)⋊(C5×ΓL(1,𝔽8))
unambiguous semidirect product(C7×C47)⋊(C5×A4)
unambiguous semidirect product(C22×C5×C47)⋊ΓL(1,𝔽8)
unambiguous semidirect product(C5×C7×C47)⋊A4

Splittings

Fitting, socle, HallC22×C5×C7×C47 ⋊ C3
derived, HallC22×C7 ⋊ C3×C5×C47
HallC5×C7×C47 ⋊ A4
HallC22×C7×C47 ⋊ C3×C5
HallC22×C5×C47 ⋊ ΓL(1,𝔽8)
HallC7×C47 ⋊ C5×A4
HallC22×C47 ⋊ C5×ΓL(1,𝔽8)
HallC22×C5×C7 ⋊ C3×C47
HallC5×C7 ⋊ A4×C47
HallC22×C5 ⋊ ΓL(1,𝔽8)×C47
SylowC7 ⋊ C5×A4×C47
SylowC22 ⋊ C5×ΓL(1,𝔽8)×C47

Subgroups

subgroupG/H
center, hypercenterC5×C47C22⋊ΓL(1,𝔽8)
commutator, cosocle, hypocenterC22×C7C3×C5×C47
FrattiniC1G
Fitting, socleC22×C5×C7×C47C3
LCSG ▷ C22×C7
UCSC1 ◁ C5×C47

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6580

Conjugacy classes & character table

2820 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19740, 87);