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C13×C41×ΓL(1,𝔽16) #44544439

order31980
automorphism?
homologyAbelianization (H1) = C4×C13×C41 · Schur multiplier (H2) = C1

Aliases

direct productC13×C41×ΓL(1,𝔽16)
unambiguous semidirect productC3⋊(C13×AGL(1,𝔽5)×C41)

Splittings

Fitting, socle, HallC3×C5×C13×C41 ⋊ C4
derived, HallC3×C5 ⋊ C4×C13×C41
HallC5×C13×C41 ⋊ Dic3
HallC3×C13×C41 ⋊ AGL(1,𝔽5)
HallC3×C5×C41 ⋊ C4×C13
HallC5×C41 ⋊ Dic3×C13
HallC3×C5×C13 ⋊ C4×C41
HallC3×C41 ⋊ C13×AGL(1,𝔽5)
HallC5×C13 ⋊ Dic3×C41
HallC3×C13 ⋊ AGL(1,𝔽5)×C41
SylowC5 ⋊ Dic3×C13×C41
SylowC3 ⋊ C13×AGL(1,𝔽5)×C41

Subgroups

subgroupG/H
center, hypercenterC13×C41ΓL(1,𝔽16)
commutator, hypocenterC3×C5C4×C13×C41
FrattiniC1G
Fitting, socleC3×C5×C13×C41C4
prime radicalC3×D5×C13×C41C2
cosocleC3×D5C2×C13×C41
LCSG ▷ C3×C5
UCSC1 ◁ C13×C41

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7995

Conjugacy classes & character table

4797 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 167);