Finite Group Databasebeta

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AGL(1,𝔽5)×#1159 #72218400

order2240
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,𝔽5)×#1159

Splittings

FittingC5×C7×D4 ⋊ C2×C4
HallC5×C7 ⋊ C4×#41
SylowC7 ⋊ #41×AGL(1,𝔽5)
SylowC5 ⋊ C4×#1159

Subgroups

subgroupG/H
center, FrattiniC2C22×D7×AGL(1,𝔽5)
commutator, socleC2×C5×C7C23×C4
FittingC5×C7×D4C2×C4
prime radicalD5×#1159C2
cosocleC2×C7×D5C24
hypercenterD4D7×AGL(1,𝔽5)
hypocenterC5×C7C4×#41
LCSG ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C2 ◁ D4

620 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

125 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#1159⋊C3, AGL(1,𝔽5)×#6474, #72218536, …
maximal normal subgroup ofAGL(1,𝔽5)×#1159⋊C3, AGL(1,𝔽5)×#6474, #72218536, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.