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C7×C31×D45 #34086117

order19530
automorphism?
homologyAbelianization (H1) = C2×C7×C31 · Schur multiplier (H2) = C1

Aliases

direct productC7×C31×D45
unambiguous semidirect productC5⋊(C7×D9×C31)
unambiguous semidirect productC9⋊(C7×D5×C31)

Splittings

Fitting, HallC5×C7×C9×C31 ⋊ C2
derived, HallC5×C9 ⋊ C2×C7×C31
HallC7×C9×C31 ⋊ D5
HallC5×C9×C31 ⋊ C2×C7
HallC5×C7×C31 ⋊ D9
HallC5×C7×C9 ⋊ C2×C31
HallC9×C31 ⋊ C7×D5
HallC5×C31 ⋊ C7×D9
HallC7×C9 ⋊ D5×C31
HallC5×C7 ⋊ D9×C31
SylowC9 ⋊ C7×D5×C31
SylowC5 ⋊ C7×D9×C31

Subgroups

subgroupG/H
center, hypercenterC7×C31D45
commutator, cosocle, hypocenterC5×C9C2×C7×C31
FrattiniC3C7×D15×C31
FittingC5×C7×C9×C31C2
socleC3×C5×C7×C31D3
LCSG ▷ C5×C9
UCSC1 ◁ C7×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9765

Conjugacy classes & character table

5208 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 22);