Finite Group Databasebeta

← Prev (#12266701) Next (#12266703) →

D5×#2403 #12266702

order1280
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C212

Aliases

direct productD5×#2403

Splittings

FittingC5×#2403 ⋊ C2
SylowC5 ⋊ C2×#2403

Subgroups

subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2403C2
hypercenter#2403D5
hypocenterC5C2×#2403
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2403

11518 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#2403, D5×#32898, #72242760, …
maximal normal subgroup ofAGL(1,𝔽5)×#2403, D5×#32898, #72242760, …
maximal quotient ofD5×#23882, D5×#23872, D5×#15258, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 336970);