Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#2158 ⋊ C2 |
| Sylow | C53 ⋊ #12841 |
358 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 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)(54,57)(55,63)(56,69)(58,75)(59,81)(60,76)(61,77)(62,83)(64,86)(65,88)(66,87)(67,90)(68,95)(70,97)(71,102)(72,98)(73,99)(74,82)(78,107)(79,109)(80,106)(84,112)(85,111)(89,113)(91,104)(92,115)(93,114)(94,110)(96,103)(100,117)(101,116)(105,108);(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)(54,56,68,94,60,72,80,101,61,73,79,100,59,71,58,70)(55,62,78,92,65,84,89,93,66,85,108,103,82,91,64,67)(57,69,95,110,76,98,106,116,77,99,109,117,81,102,75,97)(63,83,107,115,88,112,113,114,87,111,105,96,74,104,86,90);(54,55)(56,67)(57,74,77,88)(58,78)(59,65)(60,82)(61,66)(62,70)(63,76,87,81)(64,68)(69,96,99,115)(71,92)(72,103)(73,93)(75,86,106,113)(79,89)(80,108)(83,110,111,117)(84,100)(85,101)(90,98,114,102)(91,94)(95,105,109,107)(97,104,116,112)Polycyclic presentation:
2^8,53|a^2=f,b^2=dg,d^2=gh,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,e^c=eh,f^c=fh,i^c=i^521196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85762);