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C3×C29×C11⋊AGL(1,𝔽5) #34062360

order19140
automorphism?
homologyAbelianization (H1) = C3×C4×C29 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC3×C5×C11×C29 ⋊ C4
derived, HallC5×C11 ⋊ C3×C4×C29
HallC5×C11×C29 ⋊ C3×C4
HallC3×C11×C29 ⋊ AGL(1,𝔽5)
HallC3×C5×C29 ⋊ Dic11
HallC11×C29 ⋊ C3×AGL(1,𝔽5)
HallC3×C5×C11 ⋊ C4×C29
HallC5×C29 ⋊ C3×Dic11
HallC3×C11 ⋊ AGL(1,𝔽5)×C29
HallC3×C5 ⋊ C29×Dic11
SylowC11 ⋊ C3×AGL(1,𝔽5)×C29
SylowC5 ⋊ C3×C29×Dic11

Subgroups

subgroupG/H
center, hypercenterC3×C29C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C3×C4×C29
FrattiniC1G
Fitting, socleC3×C5×C11×C29C4
prime radicalC3×D5×C11×C29C2
cosocleD5×C11C2×C3×C29
LCSG ▷ C5×C11
UCSC1 ◁ C3×C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4785

Conjugacy classes & character table

2175 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 53);