Finite Group Databasebeta

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D5×#63568 #72260132

order2880
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD5×#63568

Splittings

HallC32×C5 ⋊ C2×#104
SylowC32 ⋊ D5×#104
SylowC5 ⋊ C2×#63568

Subgroups

subgroupG/H
centerC4D5×#625
commutatorC32×C4×C5C22×C4
Frattini, hypercenterC2×C4D32×D5
Fitting, cosocleC2×C32×C4×C5C23
socleC2×C32×C5C2×C22⋊C4
prime radicalC3×D5×#235C2
hypocenterC32×C5C2×#104
LCSG ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C4 ◁ C2×C4

788 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×#10590393, AGL(1,𝔽5)×#63568, #72260286
maximal normal subgroup ofD5×#10590393, AGL(1,𝔽5)×#63568, #72260286

GAP

Past the SmallGroups library coverage — no SmallGroups id.