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C11⋊((C37⋊C3)⋊D13) #44540832

order31746
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC11⋊((C37⋊C3)⋊D13)
unambiguous semidirect product(C37⋊C3)⋊D143

Splittings

Fitting, socle, derived, HallC11×C13×C37 ⋊ C2×C3
HallC11×C13×C37⋊C3 ⋊ C2
HallD5291 ⋊ C3
HallC13×C37⋊C3 ⋊ D11
HallC11×C37⋊C3 ⋊ D13
HallC13×C37 ⋊ C3×D11
HallC11×C37 ⋊ C3×D13
HallC11×C13 ⋊ D37⋊C3
HallC37⋊C3 ⋊ D143
SylowC37 ⋊ C3×D143
SylowC13 ⋊ C11⋊(D37⋊C3)
SylowC11 ⋊ (C37⋊C3)⋊D13

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C13×C37C2×C3
LCSG ▷ C11×C13×C37
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 61
transitive degreeμt(G) = 5291

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

Polycyclic presentation:

2,3,11,13,37|c^a=c^10,d^a=d^12,e^a=e^36,e^b=e^26

Conjugacy classes & character table

1077 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31746, 45);