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AGL(1,𝔽7)×#3710 #72254134

order6048
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23

Aliases

direct productAGL(1,𝔽7)×#3710

Splittings

derivedC32×C7 ⋊ C22×C3×C8
HallC32×ΓL(1,𝔽8) ⋊ C22×C8
SylowC7 ⋊ C2×C3×#3710

Subgroups

subgroupG/H
center, Frattini, hypercenterC4D32×AGL(1,𝔽7)
commutator, hypocenterC32×C7C22×C3×C8
Fitting, cosocleC32×C4×C7C23×C3
socleC2×C32×C7C22×C3×C4
prime radicalC2×C3⋊D3×AGL(1,𝔽7)C4
LCSG ▷ C32×C7
UCSC1 ◁ C4

836 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×#63818, AGL(1,𝔽7)×#63930, AGL(1,𝔽7)×#63926
maximal normal subgroup ofAGL(1,𝔽7)×#63818, AGL(1,𝔽7)×#63930, AGL(1,𝔽7)×#63926

GAP

Past the SmallGroups library coverage — no SmallGroups id.