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C47×ΓL(1,𝔽8)⋊AGL(1,𝔽5) #34089474

order19740
automorphism?
homologyAbelianization (H1) = C3×C4×C47 · Schur multiplier (H2) = C1

Aliases

direct productC47×ΓL(1,𝔽8)⋊AGL(1,𝔽5)
unambiguous semidirect productΓL(1,𝔽8)⋊(AGL(1,𝔽5)×C47)
unambiguous semidirect product(C7⋊AGL(1,𝔽5))⋊(C3×C47)
unambiguous semidirect product(C47×C7⋊AGL(1,𝔽5))⋊C3

Splittings

Fitting, socle, HallC5×C7×C47 ⋊ C3×C4
derived, HallC5×C7 ⋊ C3×C4×C47
HallC47×C7⋊AGL(1,𝔽5) ⋊ C3
HallC5×ΓL(1,𝔽8)×C47 ⋊ C4
HallΓL(1,𝔽8)×C47 ⋊ AGL(1,𝔽5)
HallC7×C47 ⋊ C3×AGL(1,𝔽5)
HallC5×C47 ⋊ ΓL(1,𝔽8)⋊C4
HallC7⋊AGL(1,𝔽5) ⋊ C3×C47
HallC5×ΓL(1,𝔽8) ⋊ C4×C47
HallΓL(1,𝔽8) ⋊ AGL(1,𝔽5)×C47
SylowC7 ⋊ C3×AGL(1,𝔽5)×C47
SylowC5 ⋊ C47×ΓL(1,𝔽8)⋊C4

Subgroups

subgroupG/H
center, hypercenterC47ΓL(1,𝔽8)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C3×C4×C47
FrattiniC1G
Fitting, socleC5×C7×C47C3×C4
prime radicalD5×ΓL(1,𝔽8)×C47C2
cosocleC7×D5C2×C3×C47
LCSG ▷ C5×C7
UCSC1 ◁ C47

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1645

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19740, 27);