Finite Group Databasebeta

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D5×#63921 #72260168

order2880
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD5×#63921

Splittings

FittingC2×C32×C4×C5 ⋊ C23
HallC32×C5 ⋊ C22×C22⋊C4
SylowC32 ⋊ C2×D5×C22⋊C4
SylowC5 ⋊ C2×#63921

Subgroups

subgroupG/H
center, FrattiniC22C2×D32×D5
commutatorC2×C32×C5C23×C4
FittingC2×C32×C4×C5C23
socle, cosocleC22×C32×C5C24
prime radicalC22×D32×D5C2
hypercenterC2×C4D32×D5
hypocenterC32×C5C22×C22⋊C4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

2932 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal quotient ofD5×#10590393

GAP

Past the SmallGroups library coverage — no SmallGroups id.