Finite Group Databasebeta

← Prev (#43244646) Next (#43244648) →

C11×Dic9×C71 #43244647

order28116
automorphism?
homologyAbelianization (H1) = C4×C11×C71 · Schur multiplier (H2) = C1

Aliases

direct productC11×Dic9×C71
unambiguous semidirect productC9⋊(C4×C11×C71)

Splittings

derived, SylowC9 ⋊ C4×C11×C71
HallC9×C11×C71 ⋊ C4
HallC9×C71 ⋊ C4×C11
HallC9×C11 ⋊ C4×C71

Subgroups

subgroupG/H
center, hypercenterC2×C11×C71D9
commutator, hypocenterC9C4×C11×C71
FrattiniC2×C3D3×C11×C71
FittingC2×C9×C11×C71C2
socle, prime radicalC2×C3×C11×C71D3
cosocleC2×C9C2×C11×C71
LCSG ▷ C9
UCSC1 ◁ C2×C11×C71

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28116

Conjugacy classes & character table

9372 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28116, 5);