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C2×D5×C7⋊C9 #11929465

order1260
isoclinismisoclinic class of D5×ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

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

Splittings

derived, HallC5×C7 ⋊ C22×C9
HallC5×C7⋊C9 ⋊ C22
HallC2×C7×D5 ⋊ C9
SylowC7 ⋊ C2×C9×D5
SylowC5 ⋊ C22×C7⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3D5×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C22×C9
FrattiniC3C2×D5×ΓL(1,𝔽8)
Fitting, socleC2×C3×C5×C7C2×C3
prime radicalC2×C3×C7×D5C3
cosocleC3×C5×C7C22×C3
LCSG ▷ C5×C7
UCSC1 ◁ C2×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 630

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×D11×C7⋊C9, C2×D5×C11×C7⋊C9, C2×C7⋊C9×D55, …
maximal normal subgroup ofC2×D5×C11×C7⋊C9, C2×D5×C13×C7⋊C9, C2×D5×C17×C7⋊C9, …
maximal quotient ofD5×D11×C7⋊C9, C2×D5×C11×C7⋊C9, C2×C7⋊C9×D55, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1260, 17);