Finite Group Databasebeta

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#100×AGL(1,𝔽13) #72259175

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

Aliases

direct product#100×AGL(1,𝔽13)

Splittings

FittingC13×#100 ⋊ C3×C4
Hall#100×#261 ⋊ C3
HallC13⋊C3 ⋊ C4×#100
SylowC13 ⋊ C3×C4×#100

Subgroups

subgroupG/H
centerC2C22⋊C4×AGL(1,𝔽13)
commutatorC22×C13C2×C3×C42
FrattiniC2×C4C22×AGL(1,𝔽13)
FittingC13×#100C3×C4
socleC2×C13C3×C4×C22⋊C4
prime radicalC2×D4×D13⋊C3C22
cosocleC2×C4×D13C23×C3
hypercenter#100AGL(1,𝔽13)
hypocenterC13C3×C4×#100
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 104

Conjugacy classes & character table

143 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.