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C2×D52×AGL(1,𝔽7) #72243152

order8400
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct productC2×D52×AGL(1,𝔽7)

Splittings

Fitting, socleC2×C52×C7 ⋊ C23×C3
derived, HallC52×C7 ⋊ C24×C3
HallC2×D52×D7 ⋊ C3
HallC52×ΓL(1,𝔽8) ⋊ C24
SylowC52 ⋊ C23×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C22×D52
SylowC7 ⋊ C22×C3×D52

Subgroups

subgroupG/H
center, hypercenterC2D52×AGL(1,𝔽7)
commutator, cosocle, hypocenterC52×C7C24×C3
FrattiniC1G
Fitting, socleC2×C52×C7C23×C3
LCSG ▷ C52×C7
UCSC1 ◁ C2

1200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 140

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽7)×D5⋊AGL(1,𝔽5), AGL(1,𝔽7)×#87886, AGL(1,𝔽7)×#87831
maximal normal subgroup ofC2×AGL(1,𝔽7)×D5⋊AGL(1,𝔽5), AGL(1,𝔽7)×#87886, AGL(1,𝔽7)×#87831
maximal quotient ofAGL(1,𝔽7)×#87886

GAP

Past the SmallGroups library coverage — no SmallGroups id.