Finite Group Databasebeta

← Prev (#13046008) Next (#13046010) →

C23×D4×AGL(1,𝔽5) #13046009

order1280
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C215

Aliases

direct productC23×D4×AGL(1,𝔽5)
unambiguous semidirect productD5⋊(C22×C4×D4)

Splittings

FittingC23×C5×D4 ⋊ C4
SylowC5 ⋊ C23×C4×D4

Subgroups

subgroupG/H
centerC24C22×AGL(1,𝔽5)
commutatorC2×C5C25×C4
FrattiniC2C25×AGL(1,𝔽5)
FittingC23×C5×D4C4
socleC24×C5C22×C4
prime radicalC23×D4×D5C2
cosocleC2×D5C26
hypercenterC23×D4AGL(1,𝔽5)
hypocenterC5C23×C4×D4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C23×D4

19998 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×D4×#1043, AGL(1,𝔽5)×#3484, AGL(1,𝔽5)×#3003, …
maximal normal subgroup ofAGL(1,𝔽5)×#3484, AGL(1,𝔽5)×#3003, C22×AGL(1,𝔽5)×#120, …
maximal quotient ofC23×D4×#1043, AGL(1,𝔽5)×#3484, AGL(1,𝔽5)×#3498, …
automorphism group of#3939, #3940, #3941, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1116277);