Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C53×#1397 ⋊ C2 |
| Sylow | C53 ⋊ #13730 |
232 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 75 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)(54,55,56,57)(60,72)(65,85)(70,93)(73,84)(74,100)(75,101)(86,115)(87,111)(94,118)(95,119)(96,105)(97,113)(102,112)(103,114)(104,121)(116,120);(58,60,71,97,62,74,98,114,81,101,117,116,91,112,79,84,64,72,88,113,82,100,78,103,63,75,99,120,77,102,61,73)(59,65,76,95,67,86,106,105,83,111,109,121,110,118,90,93,69,85,108,119,92,115,89,96,68,87,107,104,80,94,66,70);(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)(55,57)(58,59,64,69)(60,70,72,93)(61,76,79,108)(62,80,82,110)(63,83,81,68)(65,84,85,73)(66,88,90,71)(67,91,92,77)(74,104,100,121)(75,105,101,96)(78,109,98,107)(86,116,115,120)(87,103,111,114)(89,99,106,117)(94,113,118,97)(95,112,119,102)Polycyclic presentation:
2^8,53|a^2=h,b^2=df,c^2=e,d^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,f^a=fg,g^a=gh,i^a=i^52,c^b=ch2126 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90584);