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AGL(1,𝔽7)×#3717 #72254196

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

Aliases

direct productAGL(1,𝔽7)×#3717

Splittings

HallC32×ΓL(1,𝔽8) ⋊ C2×SD16
SylowC7 ⋊ C2×C3×#3717

Subgroups

subgroupG/H
centerC2AGL(1,𝔽7)×#626
commutator, Fitting, cosocleC32×C4×C7C23×C3
Frattini, hypercenterC4D32×AGL(1,𝔽7)
socleC2×C32×C7C2×C3×D4
prime radicalAGL(1,𝔽7)×C4⋊(C3⋊D3)C2
hypocenterC32×C7C2×C3×SD16
LCSG ▷ C32×C4×C7 ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C2 ◁ C4

804 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.