Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #13633 |
190 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 121 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)(58,61,65,64)(59,67,70,86)(60,73,77,76)(62,78,83,82)(63,79,85,81)(66,87,89,114)(68,90,91,110)(69,84,92,113)(71,93,96,108)(72,98,100,99)(74,101,105,104)(75,102,107,103)(80,109,111,112)(88,94,116,117)(95,106,118,121)(97,119,120,115);(58,60,72,97,63,75,78,101,61,73,98,119,79,102,83,105,65,77,100,120,85,107,82,104,64,76,99,115,81,103,62,74)(59,66,80,95,69,88,110,108,86,114,112,121,113,117,91,96,70,89,111,118,92,116,90,93,67,87,109,106,84,94,68,71);(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)(54,55,56,57)(58,59)(60,71)(61,67)(62,80)(63,84)(64,86)(65,70)(66,74)(68,72)(69,81)(73,93)(75,106)(76,108)(77,96)(78,109)(79,92)(82,112)(83,111)(85,113)(87,101)(88,115)(89,105)(90,98)(91,100)(94,97)(95,103)(99,110)(102,118)(104,114)(107,121)(116,119)(117,120)Polycyclic presentation:
2^8,53|a^2=e,b^2=df,c^2=h,d^2=fg,f^2=gh,g^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,i^a=i^523404 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90071);