Finite Group Databasebeta

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C9×(C19⋊D19)⋊C5 #44570458

order32490
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C19

Aliases

direct productC9×(C19⋊D19)⋊C5
unambiguous semidirect product(C9×C19⋊D19)⋊C5

Splittings

Fitting, HallC9×C192 ⋊ C2×C5
derived, SylowC192 ⋊ C2×C5×C9
HallC9×C192⋊C5 ⋊ C2
HallC9×C19⋊D19 ⋊ C5
HallC192⋊C5 ⋊ C2×C9
HallC19⋊D19 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC9(C19⋊D19)⋊C5
commutator, hypocenterC192C2×C5×C9
FrattiniC3C3×(C19⋊D19)⋊C5
FittingC9×C192C2×C5
socle, cosocleC3×C192C2×C3×C5
prime radicalC3×(C19⋊D19)⋊C5C3
LCSG ▷ C192
UCSC1 ◁ C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 855

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 42);