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C29⋊AGL(1,𝔽31) #41004217

order26970
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC29⋊AGL(1,𝔽31)
unambiguous semidirect product((C31⋊C3)⋊C5)⋊D29
unambiguous semidirect product(C29⋊(D31⋊C3))⋊C5
unambiguous semidirect product(C29⋊(D31⋊C5))⋊C3

Splittings

Fitting, socle, derived, HallC29×C31 ⋊ C2×C3×C5
HallC29×(C31⋊C3)⋊C5 ⋊ C2
HallC29⋊(D31⋊C5) ⋊ C3
HallC29⋊(D31⋊C3) ⋊ C5
HallC29×ΓL(1,𝔽32) ⋊ C2×C3
HallC29×C31⋊C3 ⋊ C2×C5
HallD899 ⋊ C3×C5
Hall(C31⋊C3)⋊C5 ⋊ D29
HallΓL(1,𝔽32) ⋊ C3×D29
HallC31⋊C3 ⋊ C5×D29
SylowC31 ⋊ C3×C5×D29
SylowC29 ⋊ AGL(1,𝔽31)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC29×C31C2×C3×C5
LCSG ▷ C29×C31
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 899

Polycyclic presentation:

2,3,5,29,31|d^a=d^28,e^a=e^30,e^b=e^25,e^c=e^16

Conjugacy classes & character table

269 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26970, 36);