Finite Group Databasebeta

← Prev (#72246099) Next (#72246101) →

ΓL(1,𝔽8)×#6548⋊C3 #72246100

order14112
automorphism?
homologyAbelianization (H1) = C24×C32 · Schur multiplier (H2) = C25×C3

Aliases

direct productΓL(1,𝔽8)×#6548⋊C3

Splittings

FittingC2×C72×D4 ⋊ C2×C32
HallC7×#6548 ⋊ C32
HallΓL(1,𝔽8)2 ⋊ H(5,𝔽2)
SylowC72 ⋊ C32×H(5,𝔽2)

Subgroups

subgroupG/H
center, FrattiniC2C23×ΓL(1,𝔽8)×AGL(1,𝔽7)
commutator, socle, cosocleC2×C72C24×C32
FittingC2×C72×D4C2×C32
hypercenterC2×D4ΓL(1,𝔽8)×AGL(1,𝔽7)
hypocenterC72C32×H(5,𝔽2)
LCSG ▷ C2×C72 ▷ C72
UCSC1 ◁ C2 ◁ C2×D4

2046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

305 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.