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SD16×ΓL(1,𝔽8)⋊AGL(1,𝔽7) #72245358

order14112
automorphism?
homologyAbelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3

Aliases

direct productSD16×ΓL(1,𝔽8)⋊AGL(1,𝔽7)

Splittings

FittingC72×SD16 ⋊ C2×C32
HallSD16×C7⋊D7 ⋊ C32
HallΓL(1,𝔽8)2 ⋊ C2×SD16
SylowC72 ⋊ C2×C32×SD16

Subgroups

subgroupG/H
centerC2D4×ΓL(1,𝔽8)⋊AGL(1,𝔽7)
commutator, cosocleC4×C72C23×C32
FrattiniC4C22×ΓL(1,𝔽8)⋊AGL(1,𝔽7)
FittingC72×SD16C2×C32
socleC2×C72C2×C32×D4
prime radicalD4×ΓL(1,𝔽8)⋊AGL(1,𝔽7)C2
hypercenterSD16ΓL(1,𝔽8)⋊AGL(1,𝔽7)
hypocenterC72C2×C32×SD16
LCSG ▷ C4×C72 ▷ C2×C72 ▷ C72
UCSC1 ◁ C2 ◁ C4 ◁ SD16

952 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

182 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,ℤ/8)×ΓL(1,𝔽8)⋊AGL(1,𝔽7)
maximal normal subgroup ofAGL(1,ℤ/8)×ΓL(1,𝔽8)⋊AGL(1,𝔽7)

GAP

Past the SmallGroups library coverage — no SmallGroups id.