Finite Group Databasebeta

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C37×AGL(1,𝔽31) #46806236

order34410
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C37 · Schur multiplier (H2) = C1

Aliases

direct productC37×AGL(1,𝔽31)
unambiguous semidirect product(D31⋊C3)⋊(C5×C37)
unambiguous semidirect product(D31⋊C5)⋊(C3×C37)
unambiguous semidirect product((C31⋊C3)⋊C5)⋊(C2×C37)
unambiguous semidirect product(C37×D31⋊C3)⋊C5

Splittings

Fitting, socle, HallC31×C37 ⋊ C2×C3×C5
derived, SylowC31 ⋊ C2×C3×C5×C37
HallC37×(C31⋊C3)⋊C5 ⋊ C2
HallC37×D31⋊C5 ⋊ C3
HallC37×D31⋊C3 ⋊ C5
HallC37×ΓL(1,𝔽32) ⋊ C2×C3
HallC37×C31⋊C3 ⋊ C2×C5
HallC37×D31 ⋊ C3×C5
Hall(C31⋊C3)⋊C5 ⋊ C2×C37
HallD31⋊C5 ⋊ C3×C37
HallD31⋊C3 ⋊ C5×C37
HallΓL(1,𝔽32) ⋊ C2×C3×C37
HallC31⋊C3 ⋊ C2×C5×C37
HallD31 ⋊ C3×C5×C37

Subgroups

subgroupG/H
center, hypercenterC37AGL(1,𝔽31)
commutator, cosocle, hypocenterC31C2×C3×C5×C37
FrattiniC1G
Fitting, socleC31×C37C2×C3×C5
LCSG ▷ C31
UCSC1 ◁ C37

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1147

Conjugacy classes & character table

1147 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34410, 66);