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C5×M16×AGL(1,𝔽5) #13104486

order1600
automorphism?
homologyAbelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C2×C4

Aliases

direct productC5×M16×AGL(1,𝔽5)

Splittings

FittingC52×M16 ⋊ C4
SylowC52 ⋊ C4×M16

Subgroups

subgroupG/H
centerC4×C5C22×AGL(1,𝔽5)
commutatorC2×C5C2×C42×C5
FrattiniC4C22×C5×AGL(1,𝔽5)
FittingC52×M16C4
socleC2×C52C2×C42
prime radicalC22×C5×D5C2×C4
cosocleC4×D5C23×C5
hypercenterC5×M16AGL(1,𝔽5)
hypocenterC5C4×C5×M16
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C4×C5 ◁ C5×M16

294 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

250 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×AGL(1,𝔽5)×#100, C5×AGL(1,𝔽5)×AGL(1,ℤ/8), C5×AGL(1,𝔽5)×#104, …
maximal normal subgroup ofC5×AGL(1,𝔽5)×#100, C5×AGL(1,𝔽5)×AGL(1,ℤ/8), C5×AGL(1,𝔽5)×#104
maximal quotient ofM16×AGL(1,ℤ/25)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 6838);