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C11⋊#16809817 #49146339

order36894
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC11⋊#16809817

Splittings

Fitting, socle, derived, HallC11×C13×C43 ⋊ C2×C3
HallC11×#13131976 ⋊ C2
HallD6149 ⋊ C3
Hall#13131976 ⋊ D11
HallC13×C43 ⋊ C3×D11
HallC11×C43 ⋊ D13⋊C3
HallC11×C13 ⋊ D43⋊C3
SylowC43 ⋊ C11⋊(D13⋊C3)
SylowC13 ⋊ C11⋊(D43⋊C3)
SylowC11 ⋊ #16809817

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C13×C43C2×C3
LCSG ▷ C11×C13×C43
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 67
transitive degreeμt(G) = 6149

A minimal faithful permutation representation — 2 generators on 67 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(13,17,18,14,15,19)(16,23,22,20,21,24)(26,30,31,27,28,32)(29,38,39,33,34,48)(35,51,52,41,42,60)(36,50,46,44,40,37)(43,56,58,47,49,61)(45,62,63,54,53,57)(55,65,66,64,59,67);(1,2,4,6,8,10,11,9,7,5,3)(12,13,16,15,19,22,21,23,24,18,17,20,14)(25,26,29,35,43,46,31,30,36,45,55,63,39,50,38,49,59,66,52,61,62,51,42,53,58,60,67,65,56,34,40,48,57,64,54,44,28,32,37,47,41,33,27)

Polycyclic presentation:

2,3,11,13,43|c^a=c^10,d^a=d^12,e^a=e^42,d^b=d^3,e^b=e^36

Conjugacy classes & character table

1044 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36894, 47);