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C2×AGL(1,𝔽7)×D5⋊AGL(1,𝔽5) #72243163

order16800
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×AGL(1,𝔽7)×D5⋊AGL(1,𝔽5)

Splittings

Fitting, socleC2×C52×C7 ⋊ C22×C3×C4
derived, HallC52×C7 ⋊ C23×C3×C4
HallC2×D7×D5⋊AGL(1,𝔽5) ⋊ C3
HallC52×ΓL(1,𝔽8) ⋊ C23×C4
SylowC52 ⋊ C22×C4×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C22×D5⋊AGL(1,𝔽5)
SylowC7 ⋊ C22×C3×D5⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC2AGL(1,𝔽7)×D5⋊AGL(1,𝔽5)
commutator, hypocenterC52×C7C23×C3×C4
FrattiniC1G
Fitting, socleC2×C52×C7C22×C3×C4
prime radicalC2×D52×AGL(1,𝔽7)C2
cosocleC7×C5⋊D5C24×C3
LCSG ▷ C52×C7
UCSC1 ◁ C2

2104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 140

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×#11717375
maximal normal subgroup ofAGL(1,𝔽7)×#11717375
maximal quotient ofAGL(1,𝔽7)×#11717375

GAP

Past the SmallGroups library coverage — no SmallGroups id.