Finite Group Databasebeta

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C2×C5×#15692425 #44570433

order32490
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×#15692425

Splittings

Fitting, HallC2×C5×C361 ⋊ C9
derived, SylowC361 ⋊ C2×C5×C9
HallC5×C361 ⋊ C2×C9
HallC2×C361 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5#15692425
commutator, hypocenterC361C2×C5×C9
FrattiniC19C2×C5×#4296
FittingC2×C5×C361C9
socleC2×C5×C19#4296
prime radicalC2×C5×C361⋊C3C3
cosocleC361⋊C3C2×C3×C5
LCSG ▷ C361
UCSC1 ◁ C2×C5

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3610

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 17);