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C29×C3⋊(C11⋊AGL(1,𝔽5)) #34062384

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

Aliases

direct productC29×C3⋊(C11⋊AGL(1,𝔽5))
unambiguous semidirect productC3⋊(C29×C11⋊AGL(1,𝔽5))
unambiguous semidirect productC11⋊(C29×ΓL(1,𝔽16))

Splittings

Fitting, socle, HallC3×C5×C11×C29 ⋊ C4
derived, HallC3×C5×C11 ⋊ C4×C29
HallC5×C11×C29 ⋊ Dic3
HallC3×C11×C29 ⋊ AGL(1,𝔽5)
HallC3×C5×C29 ⋊ Dic11
HallC11×C29 ⋊ ΓL(1,𝔽16)
HallC5×C29 ⋊ Dic33
HallC3×C29 ⋊ C11⋊AGL(1,𝔽5)
HallC5×C11 ⋊ Dic3×C29
HallC3×C11 ⋊ AGL(1,𝔽5)×C29
HallC3×C5 ⋊ C29×Dic11
SylowC11 ⋊ C29×ΓL(1,𝔽16)
SylowC5 ⋊ C29×Dic33
SylowC3 ⋊ C29×C11⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC29C3⋊(C11⋊AGL(1,𝔽5))
commutator, hypocenterC3×C5×C11C4×C29
FrattiniC1G
Fitting, socleC3×C5×C11×C29C4
prime radicalC3×D5×C11×C29C2
cosocleC3×D5×C11C2×C29
LCSG ▷ C3×C5×C11
UCSC1 ◁ C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4785

Conjugacy classes & character table

2001 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 77);