Finite Group Databasebeta

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D4×#87830 #72221562

order3200
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productD4×#87830

Splittings

SylowC52 ⋊ C42×D4

Subgroups

subgroupG/H
center, FrattiniC22C22×D5⋊AGL(1,𝔽5)
commutatorC2×C52C22×C42
FittingC2×C52×D4C2×C4
socleC22×C52C23×C4
prime radicalC2×D4×C5⋊D5C22
cosocleC22×C5⋊D5C24
hypercenterC2×D4D5⋊AGL(1,𝔽5)
hypocenterC52C42×D4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×D4

2274 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72221577, #72221683
maximal normal subgroup of#72221577, #72221683

GAP

Past the SmallGroups library coverage — no SmallGroups id.