Finite Group Databasebeta

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C7×C9×C11×#261 #49114454

order36036
automorphism?
homologyAbelianization (H1) = C4×C7×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×C11×#261

Splittings

Fitting, HallC7×C9×C11×C13 ⋊ C4
derived, SylowC13 ⋊ C4×C7×C9×C11
HallC9×C11×C13 ⋊ C4×C7
HallC7×C11×C13 ⋊ C4×C9
HallC7×C9×C13 ⋊ C4×C11
HallC11×C13 ⋊ C4×C7×C9
HallC9×C13 ⋊ C4×C7×C11
HallC7×C13 ⋊ C4×C9×C11

Subgroups

subgroupG/H
center, hypercenterC7×C9×C11#261
commutator, hypocenterC13C4×C7×C9×C11
FrattiniC3C3×C7×C11×#261
FittingC7×C9×C11×C13C4
socleC3×C7×C11×C13C3×C4
prime radicalC3×C7×C11×D13C2×C3
cosocleC3×D13C2×C3×C7×C11
LCSG ▷ C13
UCSC1 ◁ C7×C9×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9009

Conjugacy classes & character table

4851 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 122);