Finite Group Databasebeta

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AGL(1,𝔽5)×#64149 #72231688

order5760
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3×C4

Aliases

direct productAGL(1,𝔽5)×#64149

Splittings

FittingC2×C32×C5×D4 ⋊ C2×C4
HallC32×C5 ⋊ C4×#127
SylowC32 ⋊ AGL(1,𝔽5)×#127
SylowC5 ⋊ C4×#64149

Subgroups

subgroupG/H
center, FrattiniC22C22×C3⋊D3×AGL(1,𝔽5)
commutator, socleC22×C32×C5C23×C4
FittingC2×C32×C5×D4C2×C4
prime radicalD5×#64149C2
cosocleC22×C32×D5C24
hypercenterC2×D4C3⋊D3×AGL(1,𝔽5)
hypocenterC32×C5C4×#127
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×D4

5544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 720

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3⋊D3×AGL(1,𝔽5)×#127
maximal normal subgroup ofC3⋊D3×AGL(1,𝔽5)×#127

GAP

Past the SmallGroups library coverage — no SmallGroups id.