Finite Group Databasebeta

← Prev (#13107615) Next (#13107617) →

D5×#4130 #13107616

order1600
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productD5×#4130

Splittings

FittingC2×C4×C52 ⋊ C2×C4
SylowC52 ⋊ C2×#117

Subgroups

subgroupG/H
centerC4C2×D5×AGL(1,𝔽5)
commutator, socleC2×C52C23×C4
FrattiniC2C22×D5×AGL(1,𝔽5)
FittingC2×C4×C52C2×C4
prime radicalC22×D52C22
cosocleC2×C5×D5C24
hypercenterC2×C4D5×AGL(1,𝔽5)
hypocenterC52C2×#117
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C4 ◁ C2×C4

687 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72221505, #72221507, D5×#65767, …
maximal normal subgroup of#72221505, #72221507, D5×#65767, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 9968);