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C2×C5×D63 #11929485

order1260
isoclinismisoclinic class of D63
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D63
unambiguous semidirect product(C2×C7)⋊(C5×D9)
unambiguous semidirect product(C2×C9)⋊(C5×D7)

Splittings

FittingC2×C5×C7×C9 ⋊ C2
derived, HallC7×C9 ⋊ C22×C5
HallC5×C7×C9 ⋊ C22
HallC5×C9 ⋊ C2×D7
HallC5×C7 ⋊ C2×D9
SylowC9 ⋊ C2×C5×D7
SylowC7 ⋊ C2×C5×D9

Subgroups

subgroupG/H
center, hypercenterC2×C5D63
commutator, cosocle, hypocenterC7×C9C22×C5
FrattiniC3C2×C5×D21
FittingC2×C5×C7×C9C2
socleC2×C3×C5×C7D3
LCSG ▷ C7×C9
UCSC1 ◁ C2×C5

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 630

Conjugacy classes & character table

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

Relationships

maximal subgroup ofAGL(1,𝔽11)×D63, C2×C7⋊(C9⋊AGL(1,𝔽11)), C2×C11⋊C5×D63, …
maximal normal subgroup ofC2×C5×C11×D63, C2×C5×C13×D63, C2×C5×C17×D63, …
maximal quotient ofAGL(1,𝔽11)×D63, C2×C7⋊(C9⋊AGL(1,𝔽11)), C2×C11⋊C5×D63, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1260, 37);