Finite Group Databasebeta

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C2×#13103063 #72221341

order3200
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26×C5

Aliases

direct productC2×#13103063

Splittings

FittingC2×C52×AGL(1,ℤ/8) ⋊ C2
SylowC52 ⋊ C2×#453

Subgroups

subgroupG/H
centerC22#11717257
commutator, cosocleC2×C4×C52C24
FrattiniC2×C4C23×C5⋊D5
FittingC2×C52×AGL(1,ℤ/8)C2
socleC22×C52#120
hypercenterC2×AGL(1,ℤ/8)C5⋊D5
hypocenterC52C2×#453
LCSG ▷ C2×C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

3376 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C5⋊D5×#453
maximal normal subgroup ofC2×C5⋊D5×#453

GAP

Past the SmallGroups library coverage — no SmallGroups id.