Finite Group Databasebeta

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C2×#13099912 #72221074

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

Aliases

direct productC2×#13099912

Splittings

SylowC52 ⋊ C2×#343

Subgroups

subgroupG/H
centerC22#11716776
commutatorC22×C52C2×C42
FrattiniC2×C4C2×D5⋊AGL(1,𝔽5)
FittingC22×C4×C52C2×C4
socleC22×C52#95
prime radicalC23×C5⋊D5C2×C4
cosocleC2×C4×C5⋊D5C23
hypercenterC22×C4D5⋊AGL(1,𝔽5)
hypocenterC52C2×#343
LCSG ▷ C22×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22×C4

1282 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72213408, C2×#72213383, C2×#72213490, …
maximal normal subgroup ofC2×#72213408, C2×#72213383, C2×#72213490, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.