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C22×C9×AGL(1,𝔽5) #10623931

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

Aliases

direct productC22×C9×AGL(1,𝔽5)
unambiguous semidirect productD5⋊(C2×C4×C9)

Splittings

FittingC22×C5×C9 ⋊ C4
derived, SylowC5 ⋊ C22×C4×C9
HallC5×C9 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC22×C9AGL(1,𝔽5)
commutator, hypocenterC5C22×C4×C9
FrattiniC3C22×C3×AGL(1,𝔽5)
FittingC22×C5×C9C4
socleC22×C3×C5C3×C4
prime radicalC22×C3×D5C2×C3
cosocleC3×D5C23×C3
LCSG ▷ C5
UCSC1 ◁ C22×C9

162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×AGL(1,𝔽5))⋊Dic9, C9×(C2×AGL(1,𝔽5))⋊C4, C2×AGL(1,𝔽5)×Dic9, …
maximal normal subgroup of(C2×AGL(1,𝔽5))⋊Dic9, C9×(C2×AGL(1,𝔽5))⋊C4, C2×AGL(1,𝔽5)×Dic9, …
maximal quotient ofC2×C9×D5⋊C8, C2×C9×#700, C9×D5⋊M16, …
automorphism group ofC19×Dic5, C2×D5×C19

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 400);