Finite Group Databasebeta

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C3×C5×D3×C361 #44570445

order32490
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C361 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D3×C361
unambiguous semidirect productC3⋊(C2×C3×C5×C361)

Splittings

Fitting, HallC32×C5×C361 ⋊ C2
derivedC3 ⋊ C2×C3×C5×C361
HallC32×C361 ⋊ C2×C5
HallC32×C5 ⋊ C2×C361
SylowC32 ⋊ C2×C5×C361

Subgroups

subgroupG/H
center, hypercenterC3×C5×C361D3
commutator, hypocenterC3C2×C3×C5×C361
FrattiniC19C3×C5×D3×C19
FittingC32×C5×C361C2
socleC32×C5×C19C2×C19
prime radicalC3×C5×D3×C19C19
cosocleC3×C19C2×C3×C5×C19
LCSG ▷ C3
UCSC1 ◁ C3×C5×C361

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10830

Conjugacy classes & character table

16245 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 29);