Finite Group Databasebeta

← Prev (#44530872) Next (#44530874) →

C3×Dic11×C79⋊C3 #44530873

order31284
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×Dic11×C79⋊C3
unambiguous semidirect productC11⋊(C3×C4×C79⋊C3)
unambiguous semidirect product(Dic11×C79)⋊C32
unambiguous semidirect product(C3×Dic11×C79)⋊C3

Splittings

derived, HallC11×C79 ⋊ C32×C4
HallC3×C11×C79⋊C3 ⋊ C4
HallDic11×C79 ⋊ C32
SylowC79 ⋊ C32×Dic11
SylowC11 ⋊ C3×C4×C79⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3D11×C79⋊C3
commutator, hypocenterC11×C79C32×C4
FrattiniC2C3×D11×C79⋊C3
Fitting, socleC2×C3×C11×C79C2×C3
prime radicalC2×C3×C11×C79⋊C3C2
cosocleC2×C11×C79C2×C32
LCSG ▷ C11×C79
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10428

Conjugacy classes & character table

1218 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31284, 38);