Finite Group Databasebeta

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C2×M16×Dic11 #13077023

order1408
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×M16×Dic11

Splittings

SylowC11 ⋊ C2×C4×M16

Subgroups

subgroupG/H
centerC22×C4C22×D11
commutatorC2×C11C22×C42
FrattiniC2×C4C23×D11
FittingC22×C11×M16C2
socleC23×C11C22×C4
prime radicalC24×C11C2×C4
cosocleC2×C4×C11C24
hypercenterC22×M16D11
hypocenterC11C2×C4×M16
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×M16

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

Relationships

maximal subgroup ofDic11×H(3,ℤ/4), Dic11×#338, Dic11×#339, …
maximal normal subgroup ofDic11×H(3,ℤ/4), Dic11×#338, Dic11×#339, …
maximal quotient ofC2×M16×C11⋊C8, C2×#13066897, C2×#13066903, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 12917);