Finite Group Databasebeta

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C2×#13104783 #72220830

order3200
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#13104783

Splittings

FittingC22×C52×D4 ⋊ C4
SylowC52 ⋊ C2×#418

Subgroups

subgroupG/H
centerC22C2×C22⋊#1043
commutatorC4×C52C23×C4
FrattiniC4C23×#1043
FittingC22×C52×D4C4
socleC22×C52C2×C22⋊C4
prime radicalC22×D4×C5⋊D5C2
cosocleC4×C5⋊D5C24
hypercenterC22×D4#1043
hypocenterC52C2×#418
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

4032 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,ℤ/8)×#1043, #72221132, #72221141, …
maximal normal subgroup ofC2×AGL(1,ℤ/8)×#1043, #72221132, #72221141, …
maximal quotient of#72221141, #72223269, C2×#72220732

GAP

Past the SmallGroups library coverage — no SmallGroups id.