Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #7381 |
120 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 55 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)(55,62)(57,77)(58,71)(59,74)(60,73)(61,75)(63,91)(64,86)(65,99)(66,88)(67,87)(68,89)(69,76)(70,80)(72,78)(79,108)(81,102)(82,105)(83,104)(84,106)(85,90)(92,114)(93,101)(94,116)(95,112)(96,111)(97,113)(98,103)(100,107)(109,110)(115,117);(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)(54,55,58,64,60,66,83,95,59,67,82,96,57,76,79,107,61,68,84,97,80,63,90,92,78,65,98,94,81,93,109,115)(56,69,71,100,73,89,104,113,74,91,105,114,77,99,108,116,75,101,106,117,70,62,85,86,72,88,103,112,102,87,110,111)Polycyclic presentation:
2^8,53|a^2=d,c^2=eh,d^2=f,e^2=h,f^2=g,g^2=h,b^a=bc,c^a=ce,e^a=eh,i^a=i^52,c^b=ce,e^b=eh1544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57012);