Finite Group Databasebeta

← Prev (#49114515) Next (#49114517) →

C2×C9×C11×D91 #49114516

order36036
automorphism?
homologyAbelianization (H1) = C22×C9×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×C11×D91

Splittings

FittingC2×C7×C9×C11×C13 ⋊ C2
derived, HallC7×C13 ⋊ C22×C9×C11
HallC7×C9×C11×C13 ⋊ C22
HallC9×C11×C13 ⋊ C2×D7
HallC7×C11×C13 ⋊ C22×C9
HallC7×C9×C13 ⋊ C22×C11
HallC7×C9×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×C9×D7
HallC9×C13 ⋊ C2×C11×D7
HallC7×C11 ⋊ C2×C9×D13
HallC7×C9 ⋊ C2×C11×D13
SylowC13 ⋊ C2×C9×C11×D7
SylowC7 ⋊ C2×C9×C11×D13

Subgroups

subgroupG/H
center, hypercenterC2×C9×C11D91
commutator, hypocenterC7×C13C22×C9×C11
FrattiniC3C2×C3×C11×D91
FittingC2×C7×C9×C11×C13C2
socleC2×C3×C7×C11×C13C2×C3
prime radicalC2×C3×C11×D91C3
cosocleC3×C7×C13C22×C3×C11
LCSG ▷ C7×C13
UCSC1 ◁ C2×C9×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18018

Conjugacy classes & character table

9306 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 184);