Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #7475 |
170 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 2 generators on 117 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,56,58,71,79,102,109,116,82,103,110,115,83,107,77,99,61,70,75,100,59,72,76,101,60,73,80,105,74,98,57,69)(55,62,64,86,91,114,90,97,84,112,111,117,81,104,63,68,67,85,94,113,65,87,92,108,66,88,93,106,89,95,78,96);(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)(52,53)(54,55)(56,68,70,96)(57,64)(58,78)(59,81)(60,84)(61,67)(62,69,85,99)(63,75)(65,83)(66,82)(71,104,100,95)(72,106,102,117)(73,108,103,97)(74,91)(76,111)(77,94)(79,89)(80,90)(86,98,113,107)(87,115,114,105)(88,116,112,101)(92,110)(93,109)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=fgh,e^2=fh,f^2=gh,g^2=h,b^a=bc,c^a=cf,e^a=efgh,f^a=fg,g^a=gh,i^a=i^52,d^b=dh2132 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57279);