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C11⋊((C13⋊C3)⋊D37) #44540833

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

Aliases

unambiguous semidirect productC11⋊((C13⋊C3)⋊D37)
unambiguous semidirect product(C13⋊C3)⋊D407

Splittings

Fitting, socle, derived, HallC11×C13×C37 ⋊ C2×C3
HallC11×C37×C13⋊C3 ⋊ C2
HallD5291 ⋊ C3
HallC37×C13⋊C3 ⋊ D11
HallC13×C37 ⋊ C3×D11
HallC11×C13⋊C3 ⋊ D37
HallC11×C37 ⋊ D13⋊C3
HallC11×C13 ⋊ C3×D37
HallC13⋊C3 ⋊ D407
SylowC37 ⋊ C11⋊(D13⋊C3)
SylowC13 ⋊ C3×D407
SylowC11 ⋊ (C13⋊C3)⋊D37

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

Polycyclic presentation:

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

Conjugacy classes & character table

1429 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31746, 46);