Finite Group Databasebeta

C11×#4326 #14515483

order1936
isoclinismisoclinic class of #4323
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#4326

Splittings

SylowC112 ⋊ Q16

Subgroups

subgroupG/H
centerC2×C11C22⋊D11
commutator, cosocleC4×C11C22×C11
FrattiniC4C2×C11×D11
FittingQ8×C112C2
socle, prime radicalC2×C112D4
hypercenterQ8×C11D11
hypocenterC11C11×Q16
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C11 ◁ C4×C11 ◁ Q8×C11

66 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1936, 77);