Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #13695 |
194 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 65 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)(55,57);(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)(58,60,71,97,62,73,98,114,81,103,117,115,91,112,79,84,64,75,88,113,82,104,78,101,63,74,99,120,77,100,61,72)(59,65,76,94,67,85,106,105,83,111,109,121,110,118,90,96,69,87,108,119,92,116,89,95,68,86,107,102,80,93,66,70);(54,55)(56,57)(58,59,64,69)(60,70,75,96)(61,76,79,108)(62,80,82,110)(63,83,81,68)(65,84,87,72)(66,88,90,71)(67,91,92,77)(73,102,104,121)(74,105,103,95)(78,109,98,107)(85,115,116,120)(86,101,111,114)(89,99,106,117)(93,113,118,97)(94,112,119,100)Polycyclic presentation:
2^8,53|a^2=h,b^2=df,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^b=i^521058 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90402);