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C11×D13⋊C9 #14579451

order2574
isoclinismisoclinic class of D13⋊C3
automorphism?
homologyAbelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D13⋊C9
unambiguous semidirect productD13⋊(C9×C11)
unambiguous semidirect product(C13⋊C9)⋊(C2×C11)
unambiguous semidirect product(C11×D13)⋊C9

Splittings

derived, SylowC13 ⋊ C2×C9×C11
HallC11×C13⋊C9 ⋊ C2
HallC11×D13 ⋊ C9
HallC11×C13 ⋊ C2×C9
HallC13⋊C9 ⋊ C2×C11
HallD13 ⋊ C9×C11

Subgroups

subgroupG/H
center, hypercenterC3×C11D13⋊C3
commutator, hypocenterC13C2×C9×C11
FrattiniC3C11×D13⋊C3
Fitting, socleC3×C11×C13C2×C3
prime radicalC3×C11×D13C3
cosocleC3×C13C2×C3×C11
LCSG ▷ C13
UCSC1 ◁ C3×C11

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 1287

A minimal faithful permutation representation — 2 generators on 33 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×C11×D13⋊C9, C11×C5⋊(D13⋊C9), C11⋊C5×D13⋊C9, …
maximal normal subgroup ofC5×C11×D13⋊C9, C11⋊C5×D13⋊C9, C7×C11×D13⋊C9, …
maximal quotient ofC5×C11×D13⋊C9, C11×C5⋊(D13⋊C9), C7×C11×D13⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2574, 2);