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AGL(1,𝔽5)×C32⋊H(3,𝔽3) #72247199

order4860
automorphism?
homologyAbelianization (H1) = C33×C4 · Schur multiplier (H2) = C36

Aliases

direct productAGL(1,𝔽5)×C32⋊H(3,𝔽3)

Splittings

Fitting, HallC5×C32⋊H(3,𝔽3) ⋊ C4
SylowC5 ⋊ C4×C32⋊H(3,𝔽3)

Subgroups

subgroupG/H
center, FrattiniC32C33×AGL(1,𝔽5)
commutator, socleC32×C5C33×C4
FittingC5×C32⋊H(3,𝔽3)C4
prime radicalD5×C32⋊H(3,𝔽3)C2
cosocleC32×D5C2×C33
hypercenterC32⋊H(3,𝔽3)AGL(1,𝔽5)
hypocenterC5C4×C32⋊H(3,𝔽3)
LCSG ▷ C32×C5 ▷ C5
UCSC1 ◁ C32 ◁ C32⋊H(3,𝔽3)

1134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 135

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#10624749, AGL(1,𝔽5)×#92300, AGL(1,𝔽5)×#92338, …
maximal normal subgroup ofAGL(1,𝔽5)×#10624749, AGL(1,𝔽5)×#92300, AGL(1,𝔽5)×#92338, …
maximal quotient ofAGL(1,𝔽5)×#10624749

GAP

Past the SmallGroups library coverage — no SmallGroups id.