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C2×C5×C9×D7 #11929481

order1260
isoclinismisoclinic class of D7
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C9×D7

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9D7
commutator, hypocenterC7C22×C5×C9
FrattiniC3C2×C3×C5×D7
FittingC2×C5×C7×C9C2
socleC2×C3×C5×C7C2×C3
prime radicalC2×C3×C5×D7C3
cosocleC3×C7C22×C3×C5
LCSG ▷ C7
UCSC1 ◁ C2×C5×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 630

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC9×D7×AGL(1,𝔽11), C2×C9×C7⋊AGL(1,𝔽11), C2×C9×D7×C11⋊C5, …
maximal normal subgroup ofC2×C5×C9×C11×D7, C2×C5×C9×C13×D7, C2×C5×C9×D7×C17, …
maximal quotient ofC9×D7×AGL(1,𝔽11), C2×C9×C7⋊AGL(1,𝔽11), C2×C9×D7×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1260, 33);