Finite Group Databasebeta

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C2×C7×C9×C11×D13 #49114520

order36036
automorphism?
homologyAbelianization (H1) = C22×C7×C9×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×C9×C11×D13

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C7×C9×C11D13
commutator, hypocenterC13C22×C7×C9×C11
FrattiniC3C2×C3×C7×C11×D13
FittingC2×C7×C9×C11×C13C2
socleC2×C3×C7×C11×C13C2×C3
prime radicalC2×C3×C7×C11×D13C3
cosocleC3×C13C22×C3×C7×C11
LCSG ▷ C13
UCSC1 ◁ C2×C7×C9×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18018

Conjugacy classes & character table

11088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 188);