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C7×(D31⋊C5)⋊C9 #34086156

order19530
automorphism?
homologyAbelianization (H1) = C2×C5×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×(D31⋊C5)⋊C9
unambiguous semidirect product(D31⋊C5)⋊(C7×C9)
unambiguous semidirect product(D31⋊C9)⋊(C5×C7)
unambiguous semidirect product(ΓL(1,𝔽32)⋊C9)⋊(C2×C7)
unambiguous semidirect product(C7×D31⋊C9)⋊C5

Splittings

derived, SylowC31 ⋊ C2×C5×C7×C9
HallC7×ΓL(1,𝔽32)⋊C9 ⋊ C2
HallC7×D31⋊C9 ⋊ C5
HallC7×D31⋊C5 ⋊ C9
HallC7×C31⋊C9 ⋊ C2×C5
HallΓL(1,𝔽32)⋊C9 ⋊ C2×C7
HallC7×ΓL(1,𝔽32) ⋊ C2×C9
HallD31⋊C9 ⋊ C5×C7
HallC7×D31 ⋊ C5×C9
HallD31⋊C5 ⋊ C7×C9
HallC31⋊C9 ⋊ C2×C5×C7
HallC7×C31 ⋊ C2×C5×C9
HallΓL(1,𝔽32) ⋊ C2×C7×C9
HallD31 ⋊ C5×C7×C9

Subgroups

subgroupG/H
center, hypercenterC3×C7AGL(1,𝔽31)
commutator, hypocenterC31C2×C5×C7×C9
FrattiniC3C7×AGL(1,𝔽31)
Fitting, socleC3×C7×C31C2×C3×C5
prime radicalC3×C7×D31⋊C5C3
cosocleC3×C31C2×C3×C5×C7
LCSG ▷ C31
UCSC1 ◁ C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1953

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 61);