Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C53 ⋊ #7462 |
78 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)(54,56,69,98,59,72,99,117,82,106,110,112,80,104,78,102,61,74,100,111,79,103,77,101,60,73,76,83,58,71,57,70)(55,62,75,94,64,84,88,95,65,85,107,115,91,113,90,97,67,87,109,116,92,114,89,96,66,86,108,105,81,93,63,68);(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)(54,55,58,64,60,65,79,91,61,67,80,92,82,66,59,81)(56,68,71,94,73,95,103,115,74,97,104,116,106,96,72,105)(57,75,76,88,77,107,100,90,78,109,110,89,99,108,69,63)(62,83,84,101,85,111,113,102,87,112,114,117,86,98,93,70)Polycyclic presentation:
2^8,53|a^2=d,b^2=ce,c^2=eg,d^2=f,e^2=gh,f^2=h,g^2=h,b^a=bc,c^a=ce,e^a=eg,g^a=gh,i^b=i^521220 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57248);