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C5×D1953 #34086116

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

Aliases

direct productC5×D1953
unambiguous semidirect productC7⋊(C5×D279)
unambiguous semidirect productC9⋊(C5×D217)

Splittings

Fitting, HallC5×C7×C9×C31 ⋊ C2
derived, HallC7×C9×C31 ⋊ C2×C5
HallC5×C9×C31 ⋊ D7
HallC5×C7×C31 ⋊ D9
HallC5×C7×C9 ⋊ D31
HallC9×C31 ⋊ C5×D7
HallC7×C31 ⋊ C5×D9
HallC5×C31 ⋊ D63
HallC7×C9 ⋊ C5×D31
HallC5×C9 ⋊ D217
HallC5×C7 ⋊ D279
SylowC31 ⋊ C5×D63
SylowC9 ⋊ C5×D217
SylowC7 ⋊ C5×D279

Subgroups

subgroupG/H
center, hypercenterC5D1953
commutator, cosocle, hypocenterC7×C9×C31C2×C5
FrattiniC3C5×D651
FittingC5×C7×C9×C31C2
socleC3×C5×C7×C31D3
LCSG ▷ C7×C9×C31
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9765

Conjugacy classes & character table

4890 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 21);