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AGL(1,𝔽5)×C13⋊C3×C47 #49144015

order36660
automorphism?
homologyAbelianization (H1) = C3×C4×C47 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽5)×C13⋊C3×C47
unambiguous semidirect product(C13×AGL(1,𝔽5))⋊(C3×C47)
unambiguous semidirect product(C13×AGL(1,𝔽5)×C47)⋊C3

Splittings

Fitting, socle, HallC5×C13×C47 ⋊ C3×C4
derived, HallC5×C13 ⋊ C3×C4×C47
HallC13×AGL(1,𝔽5)×C47 ⋊ C3
HallC5×C13⋊C3×C47 ⋊ C4
HallC13×C47 ⋊ C3×AGL(1,𝔽5)
HallC13×AGL(1,𝔽5) ⋊ C3×C47
HallC5×C47 ⋊ C4×C13⋊C3
HallC5×C13⋊C3 ⋊ C4×C47
SylowC13 ⋊ C3×AGL(1,𝔽5)×C47
SylowC5 ⋊ C4×C13⋊C3×C47

Subgroups

subgroupG/H
center, hypercenterC47AGL(1,𝔽5)×C13⋊C3
commutator, hypocenterC5×C13C3×C4×C47
FrattiniC1G
Fitting, socleC5×C13×C47C3×C4
prime radicalD5×C13⋊C3×C47C2
cosocleD5×C13C2×C3×C47
LCSG ▷ C5×C13
UCSC1 ◁ C47

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3055

Conjugacy classes & character table

1645 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36660, 35);