Finite Group Databasebeta

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AGL(1,𝔽5)×#6911 #72247209

order4860
automorphism?
homologyAbelianization (H1) = C33×C4 · Schur multiplier (H2) = C34

Aliases

direct productAGL(1,𝔽5)×#6911

Splittings

Fitting, HallC5×#6911 ⋊ C4
SylowC5 ⋊ C4×#6911

Subgroups

subgroupG/H
centerC3C3×AGL(1,𝔽5)×H(3,𝔽3)
commutatorC32×C5C33×C4
FrattiniC32C33×AGL(1,𝔽5)
FittingC5×#6911C4
socleC3×C5C3×C4×H(3,𝔽3)
prime radicalD5×#6911C2
cosocleC32×D5C2×C33
hypercenter#6911AGL(1,𝔽5)
hypocenterC5C4×#6911
LCSG ▷ C32×C5 ▷ C3×C5 ▷ C5
UCSC1 ◁ C3 ◁ C33 ◁ #6911

480 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 132 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) = 135

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#10624749, AGL(1,𝔽5)×#92333, AGL(1,𝔽5)×#92285, …
maximal normal subgroup ofAGL(1,𝔽5)×#10624749, AGL(1,𝔽5)×#92333, AGL(1,𝔽5)×#92285, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.