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C11⋊((C43⋊C3)⋊D13) #49146337

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

Aliases

unambiguous semidirect productC11⋊((C43⋊C3)⋊D13)
unambiguous semidirect product(C43⋊C3)⋊D143

Splittings

Fitting, socle, derived, HallC11×C13×C43 ⋊ C2×C3
HallC11×C13×C43⋊C3 ⋊ C2
HallD6149 ⋊ C3
HallC13×C43⋊C3 ⋊ D11
HallC11×C43⋊C3 ⋊ D13
HallC13×C43 ⋊ C3×D11
HallC11×C43 ⋊ C3×D13
HallC11×C13 ⋊ D43⋊C3
HallC43⋊C3 ⋊ D143
SylowC43 ⋊ C3×D143
SylowC13 ⋊ C11⋊(D43⋊C3)
SylowC11 ⋊ (C43⋊C3)⋊D13

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)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(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)(12,13,15,17,19,21,23,24,22,20,18,16,14)(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,e^b=e^36

Conjugacy classes & character table

1220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36894, 45);