Finite Group Databasebeta

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AGL(1,𝔽5)×#4207⋊C3 #72247234

order9720
automorphism?
homologyAbelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C32

Aliases

direct productAGL(1,𝔽5)×#4207⋊C3

Splittings

Fitting, HallC5×3−1+4 ⋊ C2×C4
derivedC3×C5×C9 ⋊ C2×C32×C4
Sylow3−1+4 ⋊ C2×AGL(1,𝔽5)
SylowC5 ⋊ C4×#4207⋊C3

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, hypocenterC3×C5×C9C2×C32×C4
FrattiniC3C32×C3⋊D3×AGL(1,𝔽5)
FittingC5×3−1+4C2×C4
socleC3×C5C32×C4×C3⋊D3
prime radicalD5×#4207⋊C3C2
cosocleC3×C9×D5C22×C32
LCSG ▷ C3×C5×C9
UCSC1

1262 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 135

Conjugacy classes & character table

275 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#13091120, AGL(1,𝔽5)×(#4207⋊C2)⋊C3
maximal normal subgroup ofAGL(1,𝔽5)×(#4207⋊C2)⋊C3

GAP

Past the SmallGroups library coverage — no SmallGroups id.