Finite Group Databasebeta

← Prev (#43270652) Next (#43270654) →

C11×D7×D31⋊C3 #43270653

order28644
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×D7×D31⋊C3
unambiguous semidirect productD31⋊(C3×C11×D7)
unambiguous semidirect product(C7×D31⋊C3)⋊(C2×C11)
unambiguous semidirect product(D7×C31⋊C3)⋊(C2×C11)
unambiguous semidirect product((C31⋊C3)⋊D7)⋊(C2×C11)

Splittings

Fitting, socle, HallC7×C11×C31 ⋊ C22×C3
derived, HallC7×C31 ⋊ C22×C3×C11
HallC11×D7×D31 ⋊ C3
HallC7×C11×C31⋊C3 ⋊ C22
HallC11×C31⋊C3 ⋊ C2×D7
HallD7×D31 ⋊ C3×C11
HallC7×C31⋊C3 ⋊ C22×C11
HallC11×C31 ⋊ C2×C3×D7
HallC31⋊C3 ⋊ C2×C11×D7
HallC7×C11 ⋊ C2×D31⋊C3
SylowC31 ⋊ C2×C3×C11×D7
SylowC7 ⋊ C2×C11×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC11D7×D31⋊C3
commutator, cosocle, hypocenterC7×C31C22×C3×C11
FrattiniC1G
Fitting, socleC7×C11×C31C22×C3
LCSG ▷ C7×C31
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2387

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28644, 72);