Finite Group Databasebeta

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AGL(1,𝔽5)×#12707 #72243077

order5120
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productAGL(1,𝔽5)×#12707

Splittings

FittingC5×#12707 ⋊ C4
SylowC5 ⋊ C4×#12707

Subgroups

subgroupG/H
centerC2AGL(1,𝔽5)×#1781
commutatorC22×C4×C5C22×C42
FrattiniC22×D4C23×AGL(1,𝔽5)
FittingC5×#12707C4
socleC2×C5C4×#1781
prime radicalD5×#3484C22
cosocleC22×D4×D5C24
hypercenter#12707AGL(1,𝔽5)
hypocenterC5C4×#12707
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C23 ◁ C23×D4 ◁ #12707

16878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#511790
maximal normal subgroup ofAGL(1,𝔽5)×#511790

GAP

Past the SmallGroups library coverage — no SmallGroups id.