Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #12597 |
258 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 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)(54,57)(55,62)(56,67,68,92)(58,72)(59,74)(60,73)(61,79,66,89)(63,83)(64,85)(65,84)(69,93,78,103)(70,71,94,97)(75,100)(76,99)(77,101)(80,106,90,113)(81,82,91,96)(86,111)(87,110)(88,105)(95,98,104,108)(102,116)(107,109,114,115)(112,117);(54,56)(55,61,64,66)(57,71,73,97)(58,69)(59,70)(60,68)(62,82)(63,80,86,90)(65,81,88,91)(67,74,92,101)(72,98,99,108)(75,95)(76,78)(77,94)(79,105)(83,109)(84,89)(85,96)(87,107,112,114)(93,100,103,116)(102,104)(106,117)(110,113)(111,115);(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)(54,55,58,63,59,65,75,87,60,64,76,86,77,88,102,112)(56,66,69,90,70,91,95,114,68,61,78,80,94,81,104,107)(57,62,72,83,74,84,100,110,73,85,99,111,101,105,116,117)(67,89,93,113,71,96,98,115,92,79,103,106,97,82,108,109)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=d,e^2=g,g^2=h,b^a=bd,f^a=fh,i^a=i^52,c^b=cg,d^b=dh,f^c=fh1208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84591);