Finite Group Databasebeta

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#534×#1043 #72258336

order6400
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct product#534×#1043

Splittings

FittingC52×#534 ⋊ C4
SylowC52 ⋊ C4×#534

Subgroups

subgroupG/H
center, FrattiniC22C24×#1043
commutator, socleC22×C52C24×C4
FittingC52×#534C4
prime radicalC5⋊D5×#534C2
cosocleC22×C5⋊D5C25
hypercenter#534#1043
hypocenterC52C4×#534
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ #534

15080 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 400

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.