Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C53×#362 ⋊ C2 |
| Sylow | C53 ⋊ #33596 |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 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)(56,70)(62,85)(68,87)(69,98)(71,73)(72,101)(84,112)(86,113)(95,114)(96,109)(97,117)(99,105)(100,115)(102,104)(103,111)(106,116);(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)(54,57)(55,63)(56,69)(58,75)(59,80)(60,83)(61,77)(62,84)(64,89)(65,92)(66,94)(67,90)(68,95)(70,98)(71,99)(72,103)(73,105)(74,79)(76,81)(78,88)(82,110)(85,112)(86,97)(87,114)(91,107)(93,108)(96,116)(100,104)(101,111)(102,115)(106,109)(113,117);(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)(54,56,58,71,61,70,60,73)(55,62,64,68,67,85,66,87)(57,69,75,99,77,98,83,105)(59,72,78,102,82,101,81,104)(63,84,89,95,90,112,94,114)(65,86,91,96,93,113,79,109)(74,106,92,97,107,116,108,117)(76,100,80,103,88,115,110,111);(54,55,61,67)(56,68,70,87)(57,74,77,107)(58,66,60,64)(59,79,82,91)(62,73,85,71)(63,88,90,76)(65,78,93,81)(69,97,98,117)(72,86,101,113)(75,108,83,92)(80,94,110,89)(84,111,112,103)(95,115,114,100)(96,102,109,104)(99,106,105,116)Polycyclic presentation:
2^8,53|a^2=h,b^2=e,e^2=h,f^2=gh,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fg,g^a=gh,d^b=dh,i^b=i^52,f^c=fg,g^c=gh,i^c=i^52872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 323977);