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AGL(1,𝔽5)×#6909 #72247203

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

Aliases

direct productAGL(1,𝔽5)×#6909

Splittings

Fitting, HallC5×#6909 ⋊ C4
SylowC5 ⋊ C4×#6909

Subgroups

subgroupG/H
centerC3C3×AGL(1,𝔽5)×H(3,𝔽3)
commutatorC32×C5C33×C4
FrattiniC32C33×AGL(1,𝔽5)
FittingC5×#6909C4
socleC3×C5C3×C4×H(3,𝔽3)
prime radicalD5×#6909C2
cosocleC32×D5C2×C33
hypercenter#6909AGL(1,𝔽5)
hypocenterC5C4×#6909
LCSG ▷ C32×C5 ▷ C3×C5 ▷ C5
UCSC1 ◁ C3 ◁ C33 ◁ #6909

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

normal subgroups only

This group has 444 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)×#4183⋊C3
maximal normal subgroup ofAGL(1,𝔽5)×#10624749, AGL(1,𝔽5)×#4183⋊C3

GAP

Past the SmallGroups library coverage — no SmallGroups id.