Finite Group Databasebeta

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C2×#13103852 #72242527

order3200
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#13103852

Splittings

SylowC52 ⋊ C2×#427

Subgroups

subgroupG/H
centerC22D5⋊(C4⋊AGL(1,𝔽5))
commutatorC4×C52C23×C4
FrattiniC4C22×D5⋊AGL(1,𝔽5)
FittingC2×C52×C8C2×C4
socleC22×C52C2×C4⋊C4
prime radicalC22×D52D4
cosocleC4×C5⋊D5C24
hypercenterC2×C8D5⋊AGL(1,𝔽5)
hypocenterC52C2×#427
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

1154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72220867, #72242574, #72242587
maximal normal subgroup ofC2×#72220867, #72242574, #72242587

GAP

Past the SmallGroups library coverage — no SmallGroups id.