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D17017 #46801353

order34034
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD17017
unambiguous semidirect productC7⋊D2431
unambiguous semidirect productC11⋊D1547
unambiguous semidirect productC13⋊D1309
unambiguous semidirect productC17⋊D1001

Splittings

Fitting, socle, derived, HallC7×C11×C13×C17 ⋊ C2
HallC11×C13×C17 ⋊ D7
HallC7×C13×C17 ⋊ D11
HallC7×C11×C17 ⋊ D13
HallC7×C11×C13 ⋊ D17
HallC13×C17 ⋊ D77
HallC11×C17 ⋊ D91
HallC11×C13 ⋊ D119
HallC7×C17 ⋊ D143
HallC7×C13 ⋊ D187
HallC7×C11 ⋊ D221
SylowC17 ⋊ D1001
SylowC13 ⋊ D1309
SylowC11 ⋊ D1547
SylowC7 ⋊ D2431

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C13×C17C2
LCSG ▷ C7×C11×C13×C17
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 17017

A minimal faithful permutation representation — 2 generators on 48 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);(2,7)(3,6)(4,5)(9,18)(10,17)(11,16)(12,15)(13,14)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)(33,48)(34,47)(35,46)(36,45)(37,44)(38,43)(39,42)(40,41)

Polycyclic presentation:

2,7,11,13,17|b^a=b^6,c^a=c^10,d^a=d^12,e^a=e^16

Conjugacy classes & character table

8510 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34034, 16);