Finite Group Databasebeta

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C2×C9×C192⋊C5 #44570481

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

Aliases

direct productC2×C9×C192⋊C5
unambiguous semidirect product(C2×C9×C192)⋊C5

Splittings

Fitting, HallC2×C9×C192 ⋊ C5
derived, SylowC192 ⋊ C2×C5×C9
HallC9×C192 ⋊ C2×C5
HallC2×C192 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C9C192⋊C5
commutator, hypocenterC192C2×C5×C9
FrattiniC3C2×C3×C192⋊C5
FittingC2×C9×C192C5
socleC2×C3×C192C3×C5
prime radicalC2×C3×C192⋊C5C3
cosocleC3×C192C2×C3×C5
LCSG ▷ C192
UCSC1 ◁ C2×C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1710

Conjugacy classes & character table

1386 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 65);