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C2×C5×D3×C361 #36343113

order21660
automorphism?
homologyAbelianization (H1) = C22×C5×C361 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D3×C361
unambiguous semidirect productC3⋊(C22×C5×C361)
unambiguous semidirect product(C2×C3)⋊(C2×C5×C361)

Splittings

FittingC2×C3×C5×C361 ⋊ C2
derived, SylowC3 ⋊ C22×C5×C361
HallC3×C5×C361 ⋊ C22
HallC3×C361 ⋊ C22×C5
HallC3×C5 ⋊ C22×C361

Subgroups

subgroupG/H
center, hypercenterC2×C5×C361D3
commutator, hypocenterC3C22×C5×C361
FrattiniC19C2×C5×D3×C19
FittingC2×C3×C5×C361C2
socleC2×C3×C5×C19C2×C19
prime radicalC2×C5×D3×C19C19
cosocleC3×C19C22×C5×C19
LCSG ▷ C3
UCSC1 ◁ C2×C5×C361

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10830

Conjugacy classes & character table

10830 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21660, 37);