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C3×C5×#946 #13087957

order1440
automorphism?
homologyAbelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22

Aliases

direct productC3×C5×#946

Splittings

FittingC2×C32×C5×Q8 ⋊ C2
HallC32×C5 ⋊ C22⋊Q8
SylowC32 ⋊ C5×C22⋊Q8

Subgroups

subgroupG/H
centerC22×C3×C5C22×D3
commutator, cosocleC22×C3C23×C3×C5
FrattiniC22C22×C3×C5×D3
FittingC2×C32×C5×Q8C2
socleC22×C32×C5C23
prime radicalC22×C3×C5×D3C22
hypercenterC2×C3×C5×Q8D3
hypocenterC3C3×C5×C22⋊Q8
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C5 ◁ C2×C3×C5×Q8

334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4274);