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C7×C3⋊AGL(1,𝔽31) #34086185

order19530
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊AGL(1,𝔽31)
unambiguous semidirect productC3⋊(C7×AGL(1,𝔽31))
unambiguous semidirect product((C31⋊C3)⋊C5)⋊(D3×C7)
unambiguous semidirect product(C3⋊(D31⋊C3))⋊(C5×C7)
unambiguous semidirect product(C3⋊(D31⋊C5))⋊(C3×C7)
unambiguous semidirect product(C7×C3⋊(D31⋊C3))⋊C5

Splittings

Fitting, socleC3×C7×C31 ⋊ C2×C3×C5
derivedC3×C31 ⋊ C2×C3×C5×C7
HallC3×C7×(C31⋊C3)⋊C5 ⋊ C2
HallC7×C3⋊(D31⋊C3) ⋊ C5
HallC3×C7×C31⋊C3 ⋊ C2×C5
HallC3×(C31⋊C3)⋊C5 ⋊ C2×C7
HallC7×ΓL(1,𝔽32) ⋊ C3×D3
HallC3⋊(D31⋊C3) ⋊ C5×C7
HallC3×C31⋊C3 ⋊ C2×C5×C7
HallC7×C31 ⋊ C3×C5×D3
HallΓL(1,𝔽32) ⋊ C3×D3×C7
SylowC31 ⋊ C3×C5×D3×C7

Subgroups

subgroupG/H
center, hypercenterC7C3⋊AGL(1,𝔽31)
commutator, cosocle, hypocenterC3×C31C2×C3×C5×C7
FrattiniC1G
Fitting, socleC3×C7×C31C2×C3×C5
LCSG ▷ C3×C31
UCSC1 ◁ C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 651

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 90);