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C13×C43×ΓL(1,𝔽16) #46776561

order33540
automorphism?
homologyAbelianization (H1) = C4×C13×C43 · Schur multiplier (H2) = C1

Aliases

direct productC13×C43×ΓL(1,𝔽16)
unambiguous semidirect productC3⋊(C13×AGL(1,𝔽5)×C43)

Splittings

Fitting, socle, HallC3×C5×C13×C43 ⋊ C4
derived, HallC3×C5 ⋊ C4×C13×C43
HallC5×C13×C43 ⋊ Dic3
HallC3×C13×C43 ⋊ AGL(1,𝔽5)
HallC3×C5×C43 ⋊ C4×C13
HallC5×C43 ⋊ Dic3×C13
HallC3×C5×C13 ⋊ C4×C43
HallC3×C43 ⋊ C13×AGL(1,𝔽5)
HallC5×C13 ⋊ Dic3×C43
HallC3×C13 ⋊ AGL(1,𝔽5)×C43
SylowC5 ⋊ Dic3×C13×C43
SylowC3 ⋊ C13×AGL(1,𝔽5)×C43

Subgroups

subgroupG/H
center, hypercenterC13×C43ΓL(1,𝔽16)
commutator, hypocenterC3×C5C4×C13×C43
FrattiniC1G
Fitting, socleC3×C5×C13×C43C4
prime radicalC3×D5×C13×C43C2
cosocleC3×D5C2×C13×C43
LCSG ▷ C3×C5
UCSC1 ◁ C13×C43

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8385

Conjugacy classes & character table

5031 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 181);