Finite Group Databasebeta

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#104×AGL(1,𝔽13) #72259256

order4992
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct product#104×AGL(1,𝔽13)

Splittings

FittingC13×#104 ⋊ C3×C4
Hall#104×#261 ⋊ C3
HallC13⋊C3 ⋊ C4×#104
SylowC13 ⋊ C3×C4×#104

Subgroups

subgroupG/H
centerC4D4×AGL(1,𝔽13)
commutatorC4×C13C2×C3×C42
FrattiniC2×C4C22×AGL(1,𝔽13)
FittingC13×#104C3×C4
socleC2×C13C3×C4×C22⋊C4
prime radical#41×D13⋊C3C22
cosocleC2×C4×D13C23×C3
hypercenter#104AGL(1,𝔽13)
hypocenterC13C3×C4×#104
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 104

Conjugacy classes & character table

182 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#453×AGL(1,𝔽13)
maximal normal subgroup of#453×AGL(1,𝔽13)

GAP

Past the SmallGroups library coverage — no SmallGroups id.