Finite Group Databasebeta

← Prev (#35207497) Next (#35207499) →

C2×C7×D67⋊C11 #35207498

order20636
automorphism?
homologyAbelianization (H1) = C22×C7×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D67⋊C11
unambiguous semidirect productD67⋊(C2×C7×C11)
unambiguous semidirect product(C2×D67)⋊(C7×C11)
unambiguous semidirect product(C67⋊C11)⋊(C22×C7)
unambiguous semidirect product(C2×C67⋊C11)⋊(C2×C7)
unambiguous semidirect product(C2×C7×D67)⋊C11

Splittings

Fitting, socleC2×C7×C67 ⋊ C2×C11
derived, SylowC67 ⋊ C22×C7×C11
HallC7×C67⋊C11 ⋊ C22
HallC2×C7×D67 ⋊ C11
HallC67⋊C11 ⋊ C22×C7
HallC7×C67 ⋊ C22×C11
HallC2×D67 ⋊ C7×C11

Subgroups

subgroupG/H
center, hypercenterC2×C7D67⋊C11
commutator, cosocle, hypocenterC67C22×C7×C11
FrattiniC1G
Fitting, socleC2×C7×C67C2×C11
LCSG ▷ C67
UCSC1 ◁ C2×C7

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 938

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20636, 15);