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C7×C9×D31⋊C5 #34086121

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

Aliases

direct productC7×C9×D31⋊C5
unambiguous semidirect product(C9×D31)⋊(C5×C7)
unambiguous semidirect product(C7×C9×D31)⋊C5

Splittings

Fitting, HallC7×C9×C31 ⋊ C2×C5
derived, SylowC31 ⋊ C2×C5×C7×C9
HallC7×C9×ΓL(1,𝔽32) ⋊ C2
HallC7×C9×D31 ⋊ C5
HallC9×ΓL(1,𝔽32) ⋊ C2×C7
HallC7×ΓL(1,𝔽32) ⋊ C2×C9
HallC9×D31 ⋊ C5×C7
HallC7×D31 ⋊ C5×C9
HallC9×C31 ⋊ C2×C5×C7
HallC7×C31 ⋊ C2×C5×C9
HallΓL(1,𝔽32) ⋊ C2×C7×C9
HallD31 ⋊ C5×C7×C9

Subgroups

subgroupG/H
center, hypercenterC7×C9D31⋊C5
commutator, hypocenterC31C2×C5×C7×C9
FrattiniC3C3×C7×D31⋊C5
FittingC7×C9×C31C2×C5
socleC3×C7×C31C2×C3×C5
prime radicalC3×C7×D31⋊C5C3
cosocleC3×C31C2×C3×C5×C7
LCSG ▷ C31
UCSC1 ◁ C7×C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1953

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 26);