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AGL(1,𝔽5)×#5950 #72221900

order3840
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C24

Aliases

direct productAGL(1,𝔽5)×#5950

Splittings

FittingC5×#585 ⋊ C3×C4
HallAGL(1,𝔽5)×#585 ⋊ C3
SylowC5 ⋊ C4×#5950

Subgroups

subgroupG/H
center, hypercenterC4AGL(1,𝔽5)×C22⋊A4
commutator, hypocenterC5×H(5,𝔽2)C2×C3×C4
FrattiniC2C2×AGL(1,𝔽5)×C22⋊A4
FittingC5×#585C3×C4
socleC2×C5C2×C4×C22⋊A4
prime radicalD5×#5950C2
cosocleD5×H(5,𝔽2)C22×C3
LCSG ▷ C5×H(5,𝔽2)
UCSC1 ◁ C4

4062 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 4062 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.