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C2×C3×#6649 #13086492

order1440
isoclinismisoclinic class of #1201
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×C3×#6649

Splittings

HallC32×C5 ⋊ C2×M16
SylowC32 ⋊ C2×#676
SylowC5 ⋊ C2×C3×#208

Subgroups

subgroupG/H
center, hypercenterC2×C3×C4D3×D5
commutatorC2×C3×C5C22×C3×C4
FrattiniC4C2×C3×D3×D5
FittingC2×C32×C4×C5C22
socleC22×C32×C5C2×C4
prime radicalC22×C32×D5C4
cosocleC3×C4×C5C23×C3
hypocenterC3×C5C2×C3×M16
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C3×C4

326 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 2809);