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C2×C7×C9×D5 #11929482

order1260
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C7×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×C9×D5
unambiguous semidirect productC5⋊(C22×C7×C9)
unambiguous semidirect product(C2×C5)⋊(C2×C7×C9)

Splittings

FittingC2×C5×C7×C9 ⋊ C2
derived, SylowC5 ⋊ C22×C7×C9
HallC5×C7×C9 ⋊ C22
HallC5×C9 ⋊ C22×C7
HallC5×C7 ⋊ C22×C9

Subgroups

subgroupG/H
center, hypercenterC2×C7×C9D5
commutator, hypocenterC5C22×C7×C9
FrattiniC3C2×C3×C7×D5
FittingC2×C5×C7×C9C2
socleC2×C3×C5×C7C2×C3
prime radicalC2×C3×C7×D5C3
cosocleC3×C5C22×C3×C7
LCSG ▷ C5
UCSC1 ◁ C2×C7×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 630

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×C9×D5×D11, C2×C7×C9×D5×C11, C2×C7×C9×D55, …
maximal normal subgroup ofC2×C7×C9×D5×C11, C2×C7×C9×D5×C13, C2×C7×C9×D5×C17, …
maximal quotient ofC7×C9×D5×D11, C2×C7×C9×D5×C11, C2×C7×C9×D55, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1260, 34);