Finite Group Databasebeta

← Prev (#44526259) Next (#44526261) →

C7×C11⋊(D67⋊C3) #44526260

order30954
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11⋊(D67⋊C3)
unambiguous semidirect productC11⋊(C7×D67⋊C3)
unambiguous semidirect product(C67⋊C3)⋊(C7×D11)
unambiguous semidirect productD737⋊(C3×C7)

Splittings

Fitting, socle, HallC7×C11×C67 ⋊ C2×C3
derived, HallC11×C67 ⋊ C2×C3×C7
HallC7×C11×C67⋊C3 ⋊ C2
HallC7×D737 ⋊ C3
HallC11×C67⋊C3 ⋊ C2×C7
HallD737 ⋊ C3×C7
HallC7×C67⋊C3 ⋊ D11
HallC7×C67 ⋊ C3×D11
HallC67⋊C3 ⋊ C7×D11
HallC7×C11 ⋊ D67⋊C3
SylowC67 ⋊ C3×C7×D11
SylowC11 ⋊ C7×D67⋊C3

Subgroups

subgroupG/H
center, hypercenterC7C11⋊(D67⋊C3)
commutator, cosocle, hypocenterC11×C67C2×C3×C7
FrattiniC1G
Fitting, socleC7×C11×C67C2×C3
LCSG ▷ C11×C67
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5159

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 41);