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AGL(1,𝔽5)×C3⋊#272 #72247245

order3240
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C32

Aliases

direct productAGL(1,𝔽5)×C3⋊#272

Splittings

Fitting, derived, HallC3×C5×H(3,𝔽3) ⋊ C2×C4
SylowC3×H(3,𝔽3) ⋊ C2×AGL(1,𝔽5)
SylowC5 ⋊ C4×C3⋊#272

Subgroups

subgroupG/H
center, Frattini, hypercenterC3AGL(1,𝔽5)×C3⋊(C3⋊D3)
commutator, Fitting, hypocenterC3×C5×H(3,𝔽3)C2×C4
socleC32×C5C4×C3⋊D3
prime radicalD5×C3⋊#272C2
cosocleC3×D5×H(3,𝔽3)C22
LCSG ▷ C3×C5×H(3,𝔽3)
UCSC1 ◁ C3

766 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 90

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#92300, D3×AGL(1,𝔽5)×#272, AGL(1,𝔽5)×((C3⋊D3)⋊C3)⋊D3
maximal normal subgroup ofAGL(1,𝔽5)×#92300, D3×AGL(1,𝔽5)×#272, AGL(1,𝔽5)×((C3⋊D3)⋊C3)⋊D3
maximal quotient ofAGL(1,𝔽5)×#92338

GAP

Past the SmallGroups library coverage — no SmallGroups id.