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C11×C29×ΓL(1,𝔽16) #34062380

order19140
automorphism?
homologyAbelianization (H1) = C4×C11×C29 · Schur multiplier (H2) = C1

Aliases

direct productC11×C29×ΓL(1,𝔽16)
unambiguous semidirect productC3⋊(C11×AGL(1,𝔽5)×C29)

Splittings

Fitting, socle, HallC3×C5×C11×C29 ⋊ C4
derived, HallC3×C5 ⋊ C4×C11×C29
HallC5×C11×C29 ⋊ Dic3
HallC3×C11×C29 ⋊ AGL(1,𝔽5)
HallC3×C5×C29 ⋊ C4×C11
HallC3×C5×C11 ⋊ C4×C29
HallC5×C29 ⋊ C11×Dic3
HallC3×C29 ⋊ C11×AGL(1,𝔽5)
HallC5×C11 ⋊ Dic3×C29
HallC3×C11 ⋊ AGL(1,𝔽5)×C29
SylowC5 ⋊ C11×Dic3×C29
SylowC3 ⋊ C11×AGL(1,𝔽5)×C29

Subgroups

subgroupG/H
center, hypercenterC11×C29ΓL(1,𝔽16)
commutator, hypocenterC3×C5C4×C11×C29
FrattiniC1G
Fitting, socleC3×C5×C11×C29C4
prime radicalC3×D5×C11×C29C2
cosocleC3×D5C2×C11×C29
LCSG ▷ C3×C5
UCSC1 ◁ C11×C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4785

Conjugacy classes & character table

2871 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 73);