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C9×C11×D65 #27166014

order12870
isoclinismisoclinic class of D65
automorphism?
homologyAbelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC9×C11×D65
unambiguous semidirect productC5⋊(C9×C11×D13)

Splittings

Fitting, HallC5×C9×C11×C13 ⋊ C2
derived, HallC5×C13 ⋊ C2×C9×C11
HallC9×C11×C13 ⋊ D5
HallC5×C11×C13 ⋊ C2×C9
HallC5×C9×C13 ⋊ C2×C11
HallC5×C9×C11 ⋊ D13
HallC11×C13 ⋊ C9×D5
HallC9×C13 ⋊ D5×C11
HallC5×C11 ⋊ C9×D13
HallC5×C9 ⋊ C11×D13
SylowC13 ⋊ C9×D5×C11
SylowC5 ⋊ C9×C11×D13

Subgroups

subgroupG/H
center, hypercenterC9×C11D65
commutator, hypocenterC5×C13C2×C9×C11
FrattiniC3C3×C11×D65
FittingC5×C9×C11×C13C2
socleC3×C5×C11×C13C2×C3
prime radicalC3×C11×D65C3
cosocleC3×C5×C13C2×C3×C11
LCSG ▷ C5×C13
UCSC1 ◁ C9×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 38
transitive degreeμt(G) = 6435

A minimal faithful permutation representation — 2 generators on 38 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(15,16)(17,18)(19,20,21,22,23,24,25,26,27,28,29)(30,31,33,32,34,36,35,37,38);(1,2,4,6,8,10,12,13,11,9,7,5,3)(14,15,17,18,16)

Conjugacy classes & character table

3366 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×C11×#63122, C9×C11×#63121, C9×C11⋊#63122, …
maximal normal subgroup ofC9×C11×#63122, C9×C11×#63121, C9×C11⋊#63122, …
maximal quotient ofC9×C11×Dic65, C2×C9×C11×D65

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12870, 9);