Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #7382 |
118 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 118 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)(55,63)(57,75)(58,79)(59,85)(60,72)(61,71)(62,73)(64,89)(65,94)(66,90)(67,91)(68,97)(69,77)(70,83)(74,100)(76,106)(78,102)(80,103)(81,101)(82,110)(84,88)(86,107)(87,96)(92,115)(93,99)(95,112)(98,104)(105,108)(109,117)(111,114)(113,116);(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)(54,55,58,65,60,64,81,92,61,66,82,95,57,74,76,104,62,67,83,96,77,93,107,116,59,84,80,111,78,97,108,117)(56,68,70,98,72,63,86,87,71,89,103,113,75,90,105,114,73,100,79,109,69,91,101,94,85,99,110,115,102,88,106,112)Polycyclic presentation:
2^8,53|a^2=d,c^2=e,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=ceh,d^b=dh,e^b=eh1520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57015);