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C22×C9⋊AGL(1,𝔽5) #10623932

order720
isoclinismisoclinic class of C9⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC22×C9⋊AGL(1,𝔽5)
unambiguous semidirect productD5⋊(C2×Dic9)

Splittings

FittingC22×C5×C9 ⋊ C4
derived, HallC5×C9 ⋊ C22×C4
SylowC9 ⋊ C22×AGL(1,𝔽5)
SylowC5 ⋊ C22×Dic9

Subgroups

subgroupG/H
center, hypercenterC22C9⋊AGL(1,𝔽5)
commutator, hypocenterC5×C9C22×C4
FrattiniC3C22×ΓL(1,𝔽16)
FittingC22×C5×C9C4
socleC22×C3×C5Dic3
prime radicalC22×C3×D5D3
cosocleC9×D5C23
LCSG ▷ C5×C9
UCSC1 ◁ C22

162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×AGL(1,𝔽5))⋊Dic9, #13083994, C2×AGL(1,𝔽5)×Dic9, …
maximal normal subgroup of(C2×AGL(1,𝔽5))⋊Dic9, #13083994, C2×AGL(1,𝔽5)×Dic9, …
maximal quotient ofC2×D5⋊(C9⋊C8), C2×#10623650, D5⋊#3667, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 401);