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C3×C4⋊AGL(1,𝔽17) #72275985

order3264
automorphism?
homologyAbelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C2

Aliases

direct productC3×C4⋊AGL(1,𝔽17)

Splittings

FittingC3×C4×C17 ⋊ C16
HallC3×C17 ⋊ C4⋊C16
SylowC17 ⋊ C3×C4⋊C16

Subgroups

subgroupG/H
centerC2×C3C2×AGL(1,𝔽17)
commutatorC2×C17C2×C3×C16
FrattiniC2C2×C3×AGL(1,𝔽17)
FittingC3×C4×C17C16
socleC2×C3×C17C2×C16
prime radicalC2×C3×D17C2×C8
cosocleC2×#3633C22×C3
hypercenterC3×C4AGL(1,𝔽17)
hypocenterC17C3×C4⋊C16
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C3 ◁ C3×C4

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 204

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D4×AGL(1,𝔽17)
maximal normal subgroup ofC3×D4×AGL(1,𝔽17)

GAP

Past the SmallGroups library coverage — no SmallGroups id.