Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #7513 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 2 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)(55,61)(56,66)(63,77)(64,78)(65,79)(67,86)(68,87)(69,88)(83,99)(84,100)(85,101)(89,106)(90,107)(91,108)(105,114)(109,116);(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)(54,55,56,62,57,63,67,80,58,64,68,81,70,83,89,102,59,65,69,82,71,84,90,103,73,85,91,104,92,105,109,115,60,61,66,76,72,77,86,96,74,78,87,97,93,99,106,111,75,79,88,98,94,100,107,112,95,101,108,113,110,114,116,117)Polycyclic presentation:
2^8,53|a^2=d,d^2=e,e^2=f,f^2=g,g^2=h,b^a=bc,c^a=ch,i^a=i^52,d^b=dh2168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57379);