Finite Group Databasebeta

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D42×#1043 #72258305

order6400
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productD42×#1043

Splittings

FittingC52×D42 ⋊ C4
SylowC52 ⋊ C4×D42

Subgroups

subgroupG/H
center, FrattiniC22C24×#1043
commutator, socleC22×C52C24×C4
FittingC52×D42C4
prime radicalD42×C5⋊D5C2
cosocleC22×C5⋊D5C25
hypercenterD42#1043
hypocenterC52C4×D42
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ D42

19216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 400

Conjugacy classes & character table

250 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.