Finite Group Databasebeta

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AGL(1,𝔽5)×(#4178⋊C2)⋊C3 #72268751

order19440
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productAGL(1,𝔽5)×(#4178⋊C2)⋊C3

Splittings

Fitting, HallC5×#6911 ⋊ C22×C4
derivedC5×#732 ⋊ C22×C3×C4
Sylow#6911 ⋊ C22×AGL(1,𝔽5)
SylowC5 ⋊ C4×(#4178⋊C2)⋊C3

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, hypocenterC5×#732C22×C3×C4
FrattiniC32C3×D32×AGL(1,𝔽5)
FittingC5×#6911C22×C4
socleC3×C5C3×C4×((C3⋊D3)⋊C3)⋊C2
prime radicalD5×(#4178⋊C2)⋊C3C2
cosocleD5×#732C23×C3
LCSG ▷ C5×#732
UCSC1

1430 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 135

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.