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Dic341 #13062886

order1364
isoclinismisoclinic class of D341
automorphismAut(G) order 204600
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

dicyclicDic341
unambiguous semidirect productC11⋊Dic31
unambiguous semidirect productC31⋊Dic11

Splittings

derived, HallC11×C31 ⋊ C4
SylowC31 ⋊ Dic11
SylowC11 ⋊ Dic31

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D341
commutator, hypocenterC11×C31C4
Fitting, socle, prime radical, cosocleC2×C11×C31C2
LCSG ▷ C11×C31
UCSC1 ◁ C2

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 1364

A minimal faithful permutation representation — 2 generators on 46 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);(1,3,2,4)(6,15)(7,14)(8,13)(9,12)(10,11)(17,46)(18,45)(19,44)(20,43)(21,42)(22,41)(23,40)(24,39)(25,38)(26,37)(27,36)(28,35)(29,34)(30,33)(31,32)

Polycyclic presentation:

2^2,11,31|a^2=b,c^a=c^10,d^a=d^30

Conjugacy classes & character table

344 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×Dic341, Dic1023, C11⋊((C31⋊C3)⋊C4), …
maximal normal subgroup ofC3×Dic341, C11⋊((C31⋊C3)⋊C4), C11×Dic341, …
maximal quotient ofC3×Dic341, Dic1023, C11⋊(C31⋊#157), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1364, 3);