Finite Group Databasebeta

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C2×#72213479 #72223513

order6400
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#72213479

Splittings

SylowC52 ⋊ C2×#1856

Subgroups

subgroupG/H
centerC22#13104122
commutatorC2×C4×C52C23×C4
FrattiniC2×C4C22×D5⋊AGL(1,𝔽5)
FittingC22×C52×D4C2×C4
socleC22×C52#385
prime radicalC22×D4×C5⋊D5C22
cosocleC2×C4×C5⋊D5C24
hypercenterC22×D4D5⋊AGL(1,𝔽5)
hypocenterC52C2×#1856
LCSG ▷ C2×C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

4772 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

148 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72213584
maximal normal subgroup ofC2×#72213584

GAP

Past the SmallGroups library coverage — no SmallGroups id.