Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C53 ⋊ #7464 |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 2 generators on 117 points:
(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)(54,56,69,84,59,72,57,70,83,110,77,105,76,71,108,115,61,74,103,104,81,111,79,107,60,73,102,116,58,80,78,106)(55,62,85,109,64,87,63,68,65,88,75,98,91,96,92,99,67,90,112,117,95,86,94,101,66,89,113,97,82,114,93,100);(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)(54,55,58,64,60,65,81,91,61,67,76,95,83,66,59,82)(56,68,71,97,73,99,72,109,74,101,80,98,110,100,111,117)(57,75,69,92,78,112,102,94,79,113,103,93,108,85,77,63)(62,84,86,115,88,116,114,70,90,104,87,106,89,105,96,107)Polycyclic presentation:
2^8,53|a^2=d,b^2=ceg,c^2=egh,d^2=f,e^2=gh,f^2=h,g^2=h,b^a=bc,c^a=ce,e^a=eg,g^a=gh,d^b=dh,i^b=i^521196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57252);