Finite Group Databasebeta

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C2×(C22⋊D7)⋊AGL(1,𝔽5) #72217866

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

Aliases

direct productC2×(C22⋊D7)⋊AGL(1,𝔽5)

Splittings

FittingC23×C5×C7 ⋊ C2×C4
HallC5×C7 ⋊ C2×C4×D4
SylowC7 ⋊ C2×D4×AGL(1,𝔽5)
SylowC5 ⋊ C2×(C22⋊D7)⋊C4

Subgroups

subgroupG/H
centerC22C2×D7×AGL(1,𝔽5)
commutatorC2×C5×C7C23×C4
FrattiniC2C22×D7×AGL(1,𝔽5)
FittingC23×C5×C7C2×C4
socleC22×C5×C7C22×C4
prime radicalC2×D5×C22⋊D7C2
cosocleC2×C7×D5C24
hypercenterC23D7×AGL(1,𝔽5)
hypocenterC5×C7C2×C4×D4
LCSG ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C22 ◁ C23

852 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

134 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72217715, C2×D4×D7×AGL(1,𝔽5), #72218600, …
maximal normal subgroup ofC2×#72217715, C2×D4×D7×AGL(1,𝔽5), #72218600, …
maximal quotient of#72218596, #72218600, #72218609, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.