Finite Group Databasebeta

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D5×#64862 #72221553

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

Aliases

direct productD5×#64862

Splittings

FittingC42×C52 ⋊ C2×C4
SylowC52 ⋊ C2×#339

Subgroups

subgroupG/H
centerC4D5×C4⋊AGL(1,𝔽5)
commutatorC4×C52C2×C42
FrattiniC2×C4C2×D5×AGL(1,𝔽5)
FittingC42×C52C2×C4
socleC2×C52C2×#95
prime radicalC22×D52D4
cosocleC2×C4×C5×D5C23
hypercenterC42D5×AGL(1,𝔽5)
hypocenterC52C2×#339
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C4 ◁ C2×C4 ◁ C42

1030 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72221613, #72221622, #72221623, …
maximal normal subgroup of#72221613, #72221622, #72221623, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.