Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C53 ⋊ #7548 |
62 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 2 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)(54,55,62,84,57,64,85,108,73,93,100,106,103,111,71,79,59,66,87,105,74,95,110,116,77,90,114,117,68,78,83,97,60,63,88,112,75,89,69,81,104,109,99,92,101,107,56,61,76,91,67,80,102,115,98,96,58,65,86,113,72,94,70,82);(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)(55,61,63,79)(56,67)(57,72)(58,73)(59,76)(62,83)(64,92,89,106)(65,96,90,116)(66,97,91,82)(68,75)(69,86)(70,88)(71,87)(74,101)(77,104)(78,105,94,80)(81,109,108,93)(84,111,112,107)(85,114)(95,117,115,113)(98,99)(100,110)(102,103)Polycyclic presentation:
2^8,53|a^2=d,b^2=ceg,c^2=efh,e^2=fg,f^2=gh,g^2=h,b^a=bc,c^a=ce,e^a=ef,f^a=fg,g^a=gh,d^b=dh,i^b=i^521034 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57473);