Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #27988 |
622 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)(54,58,61,82,60,80,59,79)(55,64,66,90,67,91,65,78)(56,70,72,101,73,102,71,100)(57,75,81,107,77,105,76,104)(62,84,92,112,85,99,68,94)(63,87,74,103,89,111,88,106)(69,95,97,116,98,117,96,115)(83,108,110,114,86,109,93,113);(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)(54,57,60,77)(55,63)(56,69)(58,75,80,105)(59,76,61,81)(62,83,85,86)(64,87)(65,88)(66,74)(67,89)(68,93,92,110)(70,95)(71,96)(72,97)(73,98)(78,106)(79,104,82,107)(84,108,99,109)(90,103)(91,111)(94,113,112,114)(100,115)(101,116)(102,117);(54,56,59,71,60,73,61,72)(55,62,65,68,67,85,66,92)(57,69,76,96,77,98,81,97)(58,70,79,100,80,102,82,101)(63,86,88,110,89,83,74,93)(64,84,78,94,91,99,90,112)(75,95,104,115,105,117,107,116)(87,109,106,114,111,108,103,113);(54,55,61,65,60,67,59,66)(56,68,72,85,73,92,71,62)(57,74,76,89,77,88,81,63)(58,78,82,91,80,90,79,64)(69,86,96,93,98,83,97,110)(70,99,101,112,102,84,100,94)(75,87,104,103,105,111,107,106)(95,114,115,109,117,113,116,108)Polycyclic presentation:
2^8,53|a^2=eg,b^2=e,c^2=ef,d^2=eh,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,g^a=gh,c^b=cg,f^b=fh,g^c=gh,i^c=i^521184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 255391);