Finite Group Databasebeta

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C2×C5⋊D5×#444 #72253233

order6400
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C5

Aliases

direct productC2×C5⋊D5×#444

Splittings

FittingC2×C52×#444 ⋊ C2
SylowC52 ⋊ C22×#444

Subgroups

subgroupG/H
centerC2×C4C2×D4×C5⋊D5
commutatorC4×C52C24×C4
FrattiniC2×C4C24×C5⋊D5
FittingC2×C52×#444C2
socleC22×C52C2×C4×D4
prime radicalC2×#135×C5⋊D5C2
cosocleC2×C4×C52C25
hypercenterC2×#444C5⋊D5
hypocenterC52C22×#444
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#444

10840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 800

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×#444×#1043
maximal normal subgroup ofC2×#444×#1043

GAP

Past the SmallGroups library coverage — no SmallGroups id.