Finite Group Databasebeta

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AGL(1,𝔽5)×#88907 #72247553

order8640
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C24

Aliases

direct productAGL(1,𝔽5)×#88907

Splittings

HallC24×AGL(1,𝔽5) ⋊ 3−1+2
SylowC5 ⋊ C4×#88907

Subgroups

subgroupG/H
center, FrattiniC3C3×AGL(1,𝔽5)×C22⋊A4
commutator, socleC24×C3×C5C32×C4
FittingC24×C32×C5C3×C4
prime radicalC24×C32×D5C2×C3
cosocleC24×C3×D5C2×C32
hypercenterC32AGL(1,𝔽5)×C22⋊A4
hypocenterC24×C5C4×3−1+2
LCSG ▷ C24×C3×C5 ▷ C24×C5
UCSC1 ◁ C3 ◁ C32

2976 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 2976 conjugacy classes of subgroups — too many to draw. Only its 100 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) = 180

Conjugacy classes & character table

280 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#13049240
maximal normal subgroup ofAGL(1,𝔽5)×#13049240

GAP

Past the SmallGroups library coverage — no SmallGroups id.