Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #7545 |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 2 generators on 121 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)(58,59,66,81,61,67,85,93,75,90,100,115,98,107,73,83,63,69,87,109,76,91,102,111,79,95,113,116,99,108,74,84,64,70,88,110,77,92,112,119,104,117,121,118,105,120,101,96,78,94,103,114,97,106,72,82,62,68,86,89,71,80,60,65);(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)(54,55,56,57)(59,65)(60,66)(61,71)(62,75)(63,78)(67,89)(68,93)(69,96)(70,84)(72,100)(73,103)(74,88)(76,105)(77,99)(79,104)(80,81)(82,90)(83,94)(85,86)(87,101)(91,118)(92,116)(95,119)(97,98)(102,121)(106,115)(107,114)(108,110)(109,120)(111,117)(112,113)Polycyclic presentation:
2^8,53|a^2=d,b^2=ce,c^2=ef,e^2=fg,f^2=gh,g^2=h,b^a=bc,c^a=ce,e^a=ef,f^a=fg,g^a=gh,i^a=i^523398 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57468);