Finite Group Databasebeta

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#97×AGL(1,𝔽9) #72252955

order2304
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C2×C42

Aliases

direct product#97×AGL(1,𝔽9)

Splittings

FittingC32×#97 ⋊ C8
SylowC32 ⋊ C8×#97

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×AGL(1,𝔽9)
commutatorC2×C32C42×C8
FittingC32×#97C8
socleC22×C32C2×C4×C8
prime radicalC22×C3⋊D3C2×C42
cosocleC2×C4×#157C23
hypercenter#97AGL(1,𝔽9)
hypocenterC32C8×#97
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #97

679 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#97×AΓL(1,𝔽9)
maximal normal subgroup of#97×AΓL(1,𝔽9)

GAP

Past the SmallGroups library coverage — no SmallGroups id.