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Dic407 #13108647

order1628
isoclinismisoclinic class of D407
automorphismAut(G) order 293040
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

dicyclicDic407
unambiguous semidirect productC11⋊Dic37

Splittings

derived, HallC11×C37 ⋊ C4
SylowC37 ⋊ Dic11
SylowC11 ⋊ Dic37

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D407
commutator, hypocenterC11×C37C4
Fitting, socle, prime radical, cosocleC2×C11×C37C2
LCSG ▷ C11×C37
UCSC1 ◁ C2

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 52
transitive degreeμt(G) = 1628

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

Polycyclic presentation:

2^2,11,37|a^2=b,c^a=c^10,d^a=d^36

Conjugacy classes & character table

410 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×Dic407, Dic2849, C11⋊#13050653, …
maximal normal subgroup ofC7×Dic407, C11×Dic407, C13×Dic407, …
maximal quotient ofC7×Dic407, Dic2849, C11⋊#13050653, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1628, 3);