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D12441 #38733464

order24882
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD12441
unambiguous semidirect productC3⋊D4147
unambiguous semidirect productC11⋊D1131
unambiguous semidirect productC13⋊D957
unambiguous semidirect productC29⋊D429

Splittings

Fitting, socle, derived, HallC3×C11×C13×C29 ⋊ C2
HallC11×C13×C29 ⋊ D3
HallC3×C13×C29 ⋊ D11
HallC3×C11×C29 ⋊ D13
HallC3×C11×C13 ⋊ D29
HallC13×C29 ⋊ D33
HallC11×C29 ⋊ D39
HallC11×C13 ⋊ D87
HallC3×C29 ⋊ D143
HallC3×C13 ⋊ D319
HallC3×C11 ⋊ D377
SylowC29 ⋊ D429
SylowC13 ⋊ D957
SylowC11 ⋊ D1131
SylowC3 ⋊ D4147

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C13×C29C2
LCSG ▷ C3×C11×C13×C29
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 56
transitive degreeμt(G) = 12441

A minimal faithful permutation representation — 2 generators on 56 points:

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

Polycyclic presentation:

2,3,11,13,29|b^a=b^2,c^a=c^10,d^a=d^12,e^a=e^28

Conjugacy classes & character table

6222 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24882, 17);