Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #7240 |
148 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 63 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 — 2 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)(54,56,57,67,72,94,102,107,60,70,75,97,59,69,74,96)(55,61,62,66,64,81,71,92,65,82,85,93,90,111,101,115)(58,68,73,95,103,106,83,108,78,99,76,79,77,98,104,116)(63,86,84,109,88,113,100,117,89,80,87,91,112,110,105,114);(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)(54,55,58,63,59,64,77,88,60,65,78,89,72,90,103,112)(56,66,68,91,69,92,98,114,70,93,99,109,94,115,106,117)(57,71,73,100,74,85,104,87,75,101,76,105,102,62,83,84)(61,79,80,107,81,108,110,67,82,95,86,96,111,116,113,97)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=fgh,d^2=f,e^2=fgh,f^2=h,b^a=bc,c^a=cf,e^a=efgh,g^a=gh,i^a=i^52,d^b=dg,d^c=dh1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56665);