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Dic957 #16838567

order3828
automorphismAut(G) order 1071840
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

dicyclicDic957
unambiguous semidirect productC3⋊Dic319
unambiguous semidirect productC11⋊Dic87

Splittings

derived, HallC3×C11×C29 ⋊ C4
HallC11×C29 ⋊ Dic3
HallC3×C29 ⋊ Dic11
HallC3×C11 ⋊ Dic29
SylowC29 ⋊ Dic33
SylowC11 ⋊ Dic87
SylowC3 ⋊ Dic319

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D957
commutator, hypocenterC3×C11×C29C4
Fitting, socle, prime radical, cosocleC2×C3×C11×C29C2
LCSG ▷ C3×C11×C29
UCSC1 ◁ C2

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 3828

A minimal faithful permutation representation — 2 generators on 47 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);(1,3,2,4)(6,7)(9,18)(10,17)(11,16)(12,15)(13,14)(20,47)(21,46)(22,45)(23,44)(24,43)(25,42)(26,41)(27,40)(28,39)(29,38)(30,37)(31,36)(32,35)(33,34)

Polycyclic presentation:

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

Conjugacy classes & character table

960 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic2871, C3×Dic957, C3⋊Dic957, …
maximal normal subgroup ofC3×Dic957, C5×Dic957, C3⋊((C11⋊C5)⋊Dic29), …
maximal quotient ofDic2871, C3×Dic957, C3⋊Dic957, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3828, 8);