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Dic8415 #46777849

order33660
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

dicyclicDic8415
unambiguous semidirect productC9⋊Dic935
unambiguous semidirect productC11⋊Dic765

Splittings

derived, HallC5×C9×C11×C17 ⋊ C4
HallC9×C11×C17 ⋊ Dic5
HallC5×C11×C17 ⋊ Dic9
HallC5×C9×C17 ⋊ Dic11
HallC5×C9×C11 ⋊ Dic17
HallC11×C17 ⋊ Dic45
HallC9×C17 ⋊ Dic55
HallC9×C11 ⋊ Dic85
HallC5×C17 ⋊ Dic99
HallC5×C11 ⋊ Dic153
HallC5×C9 ⋊ Dic187
SylowC17 ⋊ Dic495
SylowC11 ⋊ Dic765
SylowC9 ⋊ Dic935
SylowC5 ⋊ Dic1683

Subgroups

subgroupG/H
center, hypercenterC2D8415
commutator, hypocenterC5×C9×C11×C17C4
FrattiniC2×C3D2805
Fitting, cosocleC2×C5×C9×C11×C17C2
socle, prime radicalC2×C3×C5×C11×C17D3
LCSG ▷ C5×C9×C11×C17
UCSC1 ◁ C2

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 33660

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)(6,13)(7,12)(8,11)(9,10)(15,18)(16,17)(20,29)(21,28)(22,27)(23,26)(24,25)(31,46)(32,45)(33,44)(34,43)(35,42)(36,41)(37,40)(38,39)

Polycyclic presentation:

2,3,5,11,17,2,3|a^2=f,b^3=g^2,b^a=b^2g,c^a=c^4,d^a=d^10,e^a=e^16,g^a=g^2

Conjugacy classes & character table

8418 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 17);