Finite Group Databasebeta

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D4×#87831 #72258577

order3200
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD4×#87831

Splittings

SylowC52 ⋊ D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D5⋊AGL(1,𝔽5)
commutator, socleC22×C52C23×C4
FittingC2×C52×D4C2×C4
prime radicalC2×D4×D52C2
cosocleC22×C5⋊D5C24
hypercenterC2×D4D5⋊AGL(1,𝔽5)
hypocenterC52D4×C22⋊C4
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×D4

2930 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72258582
maximal normal subgroup of#72258582

GAP

Past the SmallGroups library coverage — no SmallGroups id.