Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#2049 ⋊ C2 |
| Sylow | C53 ⋊ #29905 |
730 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 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)(54,58,61,80)(55,64,66,91)(56,69,70,101)(57,75,78,107)(59,79,60,82)(62,84,67,94)(63,87,88,115)(65,89,81,90)(68,97,98,100)(71,102,72,103)(73,104,92,114)(74,105,99,117)(76,106,77,108)(83,109,93,110)(85,111,95,112)(86,113,96,116);(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)(54,57,61,78)(55,63,66,88)(56,68,70,98)(58,75,80,107)(59,77,60,76)(62,83,67,93)(64,87,91,115)(65,92,81,73)(69,100,101,97)(71,74,72,99)(79,108,82,106)(84,110,94,109)(85,96,95,86)(89,114,90,104)(102,117,103,105)(111,113,112,116);(54,56,59,71,61,70,60,72)(55,62,65,85,66,67,81,95)(57,74,76,68,78,99,77,98)(58,69,79,102,80,101,82,103)(63,86,73,93,88,96,92,83)(64,84,89,111,91,94,90,112)(75,105,106,97,107,117,108,100)(87,113,104,110,115,116,114,109);(54,55)(56,67)(57,73)(58,64)(59,81)(60,65)(61,66)(62,70)(63,76)(68,96)(69,94)(71,85)(72,95)(74,83)(75,104)(77,88)(78,92)(79,90)(80,91)(82,89)(84,101)(86,98)(87,106)(93,99)(97,116)(100,113)(102,111)(103,112)(105,109)(107,114)(108,115)(110,117)Polycyclic presentation:
2^8,53|b^2=f,c^2=h,d^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,f^a=fh,c^b=cg,e^b=eh,d^c=de,f^c=fh,g^c=gh,g^d=gh,i^d=i^52632 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 277895);