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AGL(1,ℤ/8)×C5⋊D5 #13107300

order1600
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25×C5

Aliases

direct productAGL(1,ℤ/8)×C5⋊D5

Splittings

FittingC52×AGL(1,ℤ/8) ⋊ C2
SylowC52 ⋊ C2×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2C2×D4×C5⋊D5
commutator, cosocleC4×C52C24
FrattiniC4C23×C5⋊D5
FittingC52×AGL(1,ℤ/8)C2
socleC2×C52C22×D4
hypercenterAGL(1,ℤ/8)C5⋊D5
hypocenterC52C2×AGL(1,ℤ/8)
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

1192 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 1192 conjugacy classes of subgroups — too many to draw. Only its 221 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) = 200

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,ℤ/8)×#1043, C2×AGL(1,ℤ/8)×C5⋊D5, #72220846, …
maximal normal subgroup ofAGL(1,ℤ/8)×#1043, C2×AGL(1,ℤ/8)×C5⋊D5, #72220846, …
maximal quotient ofC5⋊D5×#442, C2×AGL(1,ℤ/8)×C5⋊D5, C5⋊D5×#496, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 9652);