Finite Group Databasebeta

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C2×#72253172 #72253247

order6400
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#72253172

Splittings

FittingC2×C52×#131 ⋊ C4
SylowC52 ⋊ C2×#1765

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊#1043
commutatorC4×C52C22×C42
FrattiniC2×C4C23×#1043
FittingC2×C52×#131C4
socleC22×C52C4×C22⋊C4
prime radicalC2×#41×C5⋊D5C22
cosocleC2×C4×C5⋊D5C24
hypercenterC2×#131#1043
hypocenterC52C2×#1765
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#131

6072 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 800

Conjugacy classes & character table

328 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.