Finite Group Databasebeta

← Prev (#11929051) Next (#11929053) →

Q8×AGL(1,𝔽13) #11929052

order1248
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productQ8×AGL(1,𝔽13)
unambiguous semidirect product#261⋊(C3×Q8)

Splittings

FittingQ8×C13 ⋊ C3×C4
HallQ8×#261 ⋊ C3
HallC13⋊C3 ⋊ C4×Q8
SylowC13 ⋊ C3×C4×Q8

Subgroups

subgroupG/H
center, FrattiniC2C22×AGL(1,𝔽13)
commutator, socleC2×C13C22×C3×C4
FittingQ8×C13C3×C4
prime radicalC2×D13⋊C3C23
cosocleC2×D13C23×C3
hypercenterQ8AGL(1,𝔽13)
hypocenterC13C3×C4×Q8
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ Q8

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 104

Conjugacy classes & character table

65 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#41×AGL(1,𝔽13), #72229055, SL(2,𝔽3)×AGL(1,𝔽13), …
maximal normal subgroup of#41×AGL(1,𝔽13), #72229055, SL(2,𝔽3)×AGL(1,𝔽13), …
maximal quotient of#72259353, #72259542, C4⋊C4×AGL(1,𝔽13), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 1164);