Finite Group Databasebeta

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C2×#13103983 #72223538

order3200
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13103983

Splittings

SylowC52 ⋊ C2×#389

Subgroups

subgroupG/H
centerC23C2×D5⋊AGL(1,𝔽5)
commutatorC22×C52C23×C4
FrattiniC22C22×D5⋊AGL(1,𝔽5)
FittingC22×C4×C52C2×C4
socleC23×C52C22×C4
prime radicalC23×C5⋊D5C23
cosocleC22×C5⋊D5C24
hypercenterC22×C4D5⋊AGL(1,𝔽5)
hypocenterC52C2×#389
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C23 ◁ C22×C4

1930 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal quotient of#72223539

GAP

Past the SmallGroups library coverage — no SmallGroups id.