Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #11710 |
444 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 93 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)(64,75)(69,84)(74,90)(76,92)(77,78)(80,93)(85,86)(87,91);(54,56)(55,58)(57,61)(59,60)(62,64)(63,69)(65,80)(66,78)(67,77)(68,75)(70,87)(71,86)(72,85)(73,84)(74,88)(76,82)(79,90)(81,92)(83,93)(89,91);(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)(56,60,61,58)(57,59)(62,63,66,71,68,73,67,72)(64,74,77,87,75,90,78,91)(65,79,81,70,83,88,82,89)(69,80,85,76,84,93,86,92)Polycyclic presentation:
2^8,53|a^2=e,d^2=gh,e^2=h,f^2=h,g^2=h,b^a=bd,d^a=df,f^a=fh,g^a=gh,i^a=i^52,c^b=ch,d^b=dg,e^b=efgh,f^b=fh,g^b=gh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 79827);