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AGL(1,𝔽5)×#21776 #72269867

order5120
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productAGL(1,𝔽5)×#21776

Splittings

FittingC5×#21776 ⋊ C4
SylowC5 ⋊ C4×#21776

Subgroups

subgroupG/H
centerC2AGL(1,𝔽5)×#2308
commutatorC23×C5C23×C42
FrattiniC24C24×AGL(1,𝔽5)
FittingC5×#21776C4
socleC2×C5C4×#2308
prime radicalD5×#3484C22
cosocleC24×D5C25
hypercenter#21776AGL(1,𝔽5)
hypocenterC5C4×#21776
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C24 ◁ #21776

21750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.