Finite Group Databasebeta

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C2×C5⋊D5×#509 #72253271

order6400
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29×C5

Aliases

direct productC2×C5⋊D5×#509

Splittings

FittingC2×C52×#509 ⋊ C2
SylowC52 ⋊ C22×#509

Subgroups

subgroupG/H
centerC22C2×D8×C5⋊D5
commutator, cosocleC52×C8C25
FrattiniC8C24×C5⋊D5
FittingC2×C52×#509C2
socleC22×C52C22×D8
hypercenterC2×#509C5⋊D5
hypocenterC52C22×#509
LCSG ▷ C52×C8 ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

9336 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 800

Conjugacy classes & character table

448 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×#509×#1043
maximal normal subgroup ofC2×#509×#1043

GAP

Past the SmallGroups library coverage — no SmallGroups id.