Finite Group Databasebeta

C5×#4131 #11717413

order800
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#4131

Splittings

SylowC52 ⋊ #131

Subgroups

subgroupG/H
centerC2×C5C22×AGL(1,𝔽5)
commutatorC2×C5C22×C4×C5
FrattiniC2C22×C5×AGL(1,𝔽5)
FittingC52×D4C4
socleC2×C52C22×C4
prime radicalC5×#711C2
cosocleDic5C23×C5
hypercenterC5×D4AGL(1,𝔽5)
hypocenterC5C5×#131
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C5 ◁ C5×D4

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

125 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13103731, #13103732, #13103733, …
maximal normal subgroup of#13103731, #13103732, #13103733, …
maximal quotient ofC5×#65691, C5×#65692, C5×#65693, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(800, 1072);