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C2×M16×Dic5 #10615476

order640
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×M16×Dic5

Splittings

SylowC5 ⋊ C2×C4×M16

Subgroups

subgroupG/H
centerC22×C4C22×D5
commutatorC2×C5C22×C42
FrattiniC2×C4C23×D5
FittingC22×C5×M16C2
socleC23×C5C22×C4
prime radicalC24×C5C2×C4
cosocleC2×C4×C5C24
hypercenterC22×M16D5
hypocenterC5C2×C4×M16
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C22×M16

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic5×H(3,ℤ/4), Dic5×#338, Dic5×#339, …
maximal normal subgroup ofDic5×H(3,ℤ/4), Dic5×#338, Dic5×#339, …
maximal quotient ofC2×M16×#168, C2×#10601532, C2×#10600640, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(640, 17558);