Finite Group Databasebeta

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C2×D7×C4⋊AGL(1,𝔽5) #72217877

order2240
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×D7×C4⋊AGL(1,𝔽5)

Splittings

FittingC2×C4×C5×C7 ⋊ C2×C4
HallC5×C7 ⋊ C22×C4⋊C4
SylowC7 ⋊ C22×C4⋊AGL(1,𝔽5)
SylowC5 ⋊ C2×D7×C4⋊C4

Subgroups

subgroupG/H
centerC22C2×D7×AGL(1,𝔽5)
commutatorC2×C5×C7C23×C4
FrattiniC2C22×D7×AGL(1,𝔽5)
FittingC2×C4×C5×C7C2×C4
socleC22×C5×C7C22×C4
prime radicalC22×D5×D7C22
cosocleC2×C7×D5C24
hypercenterC2×C4D7×AGL(1,𝔽5)
hypocenterC5×C7C22×C4⋊C4
LCSG ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C22 ◁ C2×C4

836 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽7)×C4⋊AGL(1,𝔽5), C2×D4×D7×AGL(1,𝔽5), D7×#65727, …
maximal normal subgroup ofC2×AGL(1,𝔽7)×C4⋊AGL(1,𝔽5), C2×D4×D7×AGL(1,𝔽5), D7×#65727, …
maximal quotient ofD7×#65727, D7×#65699

GAP

Past the SmallGroups library coverage — no SmallGroups id.