Finite Group Databasebeta

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C2×#13099900 #72221044

order3200
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#13099900

Splittings

SylowC52 ⋊ C2×#339

Subgroups

subgroupG/H
centerC2×C4#87831
commutatorC4×C52C2×C42
FrattiniC2×C4C2×D5⋊AGL(1,𝔽5)
FittingC22×C4×C52C2×C4
socleC22×C52#95
prime radicalC23×C5⋊D5D4
cosocleC2×C4×C5⋊D5C23
hypercenterC22×C4D5⋊AGL(1,𝔽5)
hypocenterC52C2×#339
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C4 ◁ C22×C4

1474 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72213321, C2×#72213408, #72223116, …
maximal normal subgroup ofC2×#72213321, C2×#72213408, #72223116, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.