Finite Group Databasebeta

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C2×C3×C5×(C2×D3)⋊C4 #13087938

order1440
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC2×C3×C5×(C2×D3)⋊C4

Splittings

FittingC22×C32×C4×C5 ⋊ C2
HallC32×C5 ⋊ C2×C22⋊C4
SylowC32 ⋊ C2×C5×C22⋊C4

Subgroups

subgroupG/H
centerC23×C3×C5C2×D3
commutatorC2×C3C22×C3×C4×C5
FrattiniC22C22×C3×C5×D3
FittingC22×C32×C4×C5C2
socleC23×C32×C5C22
prime radicalC23×C3×C5×D3C2
cosocleC22×C3C23×C3×C5
hypercenterC22×C3×C4×C5D3
hypocenterC3C2×C3×C5×C22⋊C4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3×C5 ◁ C22×C3×C4×C5

582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4255);