Finite Group Databasebeta

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D5×#10604614 #72258462

order6400
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD5×#10604614

Splittings

FittingC52×#127 ⋊ C2×C4
SylowC52 ⋊ C2×#1887

Subgroups

subgroupG/H
centerC2D5×#65779
commutatorC2×C4×C52C23×C4
FrattiniC2×C4C22×D5×AGL(1,𝔽5)
FittingC52×#127C2×C4
socleC2×C52C2×#386
prime radicalD52×#127C2
cosocleC2×C4×C5×D5C24
hypercenter#127D5×AGL(1,𝔽5)
hypocenterC52C2×#1887
LCSG ▷ C2×C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2 ◁ C2×C4 ◁ #127

5301 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.