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C2×C5×C9×D173 #44528146

order31140
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C9×D173
unambiguous semidirect productC173⋊(C22×C5×C9)
unambiguous semidirect product(C2×C173)⋊(C2×C5×C9)

Splittings

FittingC2×C5×C9×C173 ⋊ C2
derived, SylowC173 ⋊ C22×C5×C9
HallC5×C9×C173 ⋊ C22
HallC9×C173 ⋊ C22×C5
HallC5×C173 ⋊ C22×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9D173
commutator, hypocenterC173C22×C5×C9
FrattiniC3C2×C3×C5×D173
FittingC2×C5×C9×C173C2
socleC2×C3×C5×C173C2×C3
prime radicalC2×C3×C5×D173C3
cosocleC3×C173C22×C3×C5
LCSG ▷ C173
UCSC1 ◁ C2×C5×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15570

Conjugacy classes & character table

7920 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31140, 36);