Finite Group Databasebeta

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AGL(1,𝔽5)×#10595100 #72259387

order11520
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productAGL(1,𝔽5)×#10595100

Splittings

FittingC2×C32×C5×D4 ⋊ C22×C4
HallC32×C5 ⋊ C2×C4×AGL(1,ℤ/8)
SylowC32 ⋊ C2×AGL(1,𝔽5)×AGL(1,ℤ/8)
SylowC5 ⋊ C4×#10595100

Subgroups

subgroupG/H
centerC2C2×AGL(1,𝔽5)×#3811
commutatorC32×C4×C5C24×C4
FrattiniC4C22×D32×AGL(1,𝔽5)
FittingC2×C32×C5×D4C22×C4
socleC2×C32×C5C22×C4×D4
prime radicalD5×#10595100C2
cosocleC32×C4×D5C25
hypercenterC2×D4D32×AGL(1,𝔽5)
hypocenterC32×C5C2×C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

15496 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

270 conjugacy classes. The character table is too large to display.

Relationships

holomorph ofC5×C3⋊C8

GAP

Past the SmallGroups library coverage — no SmallGroups id.