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C5×C9×C19⋊D19 #44570494

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

Aliases

direct productC5×C9×C19⋊D19

Splittings

Fitting, HallC5×C9×C192 ⋊ C2
derived, SylowC192 ⋊ C2×C5×C9
HallC9×C192 ⋊ C2×C5
HallC5×C192 ⋊ C2×C9

Subgroups

subgroupG/H
center, hypercenterC5×C9C19⋊D19
commutator, hypocenterC192C2×C5×C9
FrattiniC3C3×C5×C19⋊D19
FittingC5×C9×C192C2
socleC3×C5×C192C2×C3
prime radicalC3×C5×C19⋊D19C3
cosocleC3×C192C2×C3×C5
LCSG ▷ C192
UCSC1 ◁ C5×C9

264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16245

Conjugacy classes & character table

8190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 78);