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AGL(1,𝔽5)×#1159⋊C3 #72218402

order6720
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,𝔽5)×#1159⋊C3

Splittings

FittingC5×C7×D4 ⋊ C2×C3×C4
HallAGL(1,𝔽5)×#1159 ⋊ C3
HallC5×ΓL(1,𝔽8) ⋊ C4×#41
HallC5×C7 ⋊ C3×C4×#41
HallΓL(1,𝔽8) ⋊ #41×AGL(1,𝔽5)
SylowC7 ⋊ C3×#41×AGL(1,𝔽5)
SylowC5 ⋊ C4×#1159⋊C3

Subgroups

subgroupG/H
center, FrattiniC2C22×AGL(1,𝔽5)×AGL(1,𝔽7)
commutator, socleC2×C5×C7C23×C3×C4
FittingC5×C7×D4C2×C3×C4
prime radicalD5×#1159⋊C3C2
cosocleC2×C7×D5C24×C3
hypercenterD4AGL(1,𝔽5)×AGL(1,𝔽7)
hypocenterC5×C7C3×C4×#41
LCSG ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C2 ◁ D4

1240 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#6474⋊C3, #72218540, #41×AGL(1,𝔽5)×AGL(1,𝔽7)
maximal normal subgroup ofAGL(1,𝔽5)×#6474⋊C3, #72218540, #41×AGL(1,𝔽5)×AGL(1,𝔽7)

GAP

Past the SmallGroups library coverage — no SmallGroups id.