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AGL(1,𝔽5)×#12068 #72242129

order5120
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productAGL(1,𝔽5)×#12068

Splittings

FittingC5×#12068 ⋊ C4
SylowC5 ⋊ C4×#12068

Subgroups

subgroupG/H
centerC4AGL(1,𝔽5)×#442
commutatorC5×C8C22×C4×C8
FrattiniC4×C8C23×AGL(1,𝔽5)
FittingC5×#12068C4
socleC2×C5C4×#1580
prime radicalD5×#508C2×C4
cosocleC4×C8×D5C24
hypercenter#12068AGL(1,𝔽5)
hypocenterC5C4×#12068
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4 ◁ C2×C8 ◁ #346 ◁ #12068

2206 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×AGL(1,ℤ/32)
maximal normal subgroup ofAGL(1,𝔽5)×AGL(1,ℤ/32)

GAP

Past the SmallGroups library coverage — no SmallGroups id.