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C9×C11×Dic91 #49114342

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

Aliases

direct productC9×C11×Dic91

Splittings

derived, HallC7×C13 ⋊ C4×C9×C11
HallC7×C9×C11×C13 ⋊ C4
HallC9×C11×C13 ⋊ Dic7
HallC7×C11×C13 ⋊ C4×C9
HallC7×C9×C13 ⋊ C4×C11
HallC7×C9×C11 ⋊ Dic13
HallC11×C13 ⋊ C9×Dic7
HallC9×C13 ⋊ C11×Dic7
HallC7×C11 ⋊ C9×Dic13
HallC7×C9 ⋊ C11×Dic13
SylowC13 ⋊ C9×C11×Dic7
SylowC7 ⋊ C9×C11×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C9×C11D91
commutator, hypocenterC7×C13C4×C9×C11
FrattiniC2×C3C3×C11×D91
FittingC2×C7×C9×C11×C13C2
socle, prime radicalC2×C3×C7×C11×C13C2×C3
cosocleC2×C3×C7×C13C2×C3×C11
LCSG ▷ C7×C13
UCSC1 ◁ C2×C9×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 36036

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, 10);