Finite Group Databasebeta

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AGL(1,𝔽5)×#60399 #72269828

order5120
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C215

Aliases

direct productAGL(1,𝔽5)×#60399

Splittings

FittingC5×#60399 ⋊ C4
SylowC5 ⋊ C4×#60399

Subgroups

subgroupG/H
centerC2C22×AGL(1,𝔽5)×#120
commutatorC23×C5C25×C4
FrattiniC23C25×AGL(1,𝔽5)
FittingC5×#60399C4
socleC2×C5C22×C4×#120
prime radicalD5×#60399C2
cosocleC23×D5C26
hypercenter#60399AGL(1,𝔽5)
hypocenterC5C4×#60399
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C22×D4 ◁ #60399

Only the 7908 normal subgroups are shown; non-normal subgroups are omitted.

Full subgroup data →

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.