Finite Group Databasebeta

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C2×C9×C11×C13×D7 #49114517

order36036
automorphism?
homologyAbelianization (H1) = C22×C9×C11×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×C11×C13×D7

Splittings

FittingC2×C7×C9×C11×C13 ⋊ C2
derived, SylowC7 ⋊ C22×C9×C11×C13
HallC7×C9×C11×C13 ⋊ C22
HallC7×C11×C13 ⋊ C22×C9
HallC7×C9×C13 ⋊ C22×C11
HallC7×C9×C11 ⋊ C22×C13
HallC7×C13 ⋊ C22×C9×C11
HallC7×C11 ⋊ C22×C9×C13
HallC7×C9 ⋊ C22×C11×C13

Subgroups

subgroupG/H
center, hypercenterC2×C9×C11×C13D7
commutator, hypocenterC7C22×C9×C11×C13
FrattiniC3C2×C3×C11×C13×D7
FittingC2×C7×C9×C11×C13C2
socleC2×C3×C7×C11×C13C2×C3
prime radicalC2×C3×C11×C13×D7C3
cosocleC3×C7C22×C3×C11×C13
LCSG ▷ C7
UCSC1 ◁ C2×C9×C11×C13

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18018

Conjugacy classes & character table

12870 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 185);