Finite Group Databasebeta

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C2×#13107772 #72242664

order3200
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C5

Aliases

direct productC2×#13107772

Splittings

SylowC52 ⋊ C22×#131

Subgroups

subgroupG/H
centerC2×C4C22×#1044
commutatorC2×C52C24×C4
FrattiniC2C24×#1044
FittingC2×C52×#41C4
socleC22×C52C23×C4
prime radicalC2×#41×C5⋊D5C2
cosocle#1039C25
hypercenterC2×#41#1044
hypocenterC52C22×#131
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C4 ◁ C2×#41

3898 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72221297, C2×#72221300, #72242691
maximal normal subgroup ofC2×#72221297, C2×#72221300, #72242691

GAP

Past the SmallGroups library coverage — no SmallGroups id.