Finite Group Databasebeta

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C2×M16×Dic13 #13123243

order1664
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×M16×Dic13

Splittings

SylowC13 ⋊ C2×C4×M16

Subgroups

subgroupG/H
centerC22×C4C22×D13
commutatorC2×C13C22×C42
FrattiniC2×C4C23×D13
FittingC22×C13×M16C2
socleC23×C13C22×C4
prime radicalC24×C13C2×C4
cosocleC2×C4×C13C24
hypercenterC22×M16D13
hypocenterC13C2×C4×M16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×M16

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofDic13×H(3,ℤ/4), Dic13×#338, Dic13×#339, …
maximal normal subgroup ofDic13×H(3,ℤ/4), Dic13×#338, Dic13×#339, …
maximal quotient ofC2×M16×#1055, C2×#13113117, C2×#13113123, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 12917);