Finite Group Databasebeta

C5×#66084 #13106904

order1600
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#66084

Splittings

FittingC52×#131 ⋊ C2
SylowC52 ⋊ #568

Subgroups

subgroupG/H
centerC4×C5C23×D5
commutatorC2×C5C23×C4×C5
FrattiniC4C23×C5×D5
FittingC52×#131C2
socleC2×C52C23×C4
prime radicalC5×D5×#41C2
cosocleC4×C5C24×C5
hypercenterC5×#131D5
hypocenterC5C5×#568
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C4×C5 ◁ C5×#131

578 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 9256);