Finite Group Databasebeta

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C9×C11×D7×D13 #49114458

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

Aliases

direct productC9×C11×D7×D13

Splittings

Fitting, HallC7×C9×C11×C13 ⋊ C22
derived, HallC7×C13 ⋊ C22×C9×C11
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, hypercenterC9×C11D7×D13
commutator, hypocenterC7×C13C22×C9×C11
FrattiniC3C3×C11×D7×D13
FittingC7×C9×C11×C13C22
socleC3×C7×C11×C13C22×C3
prime radicalC3×C11×D7×D13C3
cosocleC3×C7×C13C22×C3×C11
LCSG ▷ C7×C13
UCSC1 ◁ C9×C11

120 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9009

Conjugacy classes & character table

3960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 126);