Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C53×#1400 ⋊ C2 |
| Sylow | C53 ⋊ #7337 |
154 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 45 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:
(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)(54,56)(55,62)(57,73)(58,76)(59,70)(60,68)(61,71)(63,86)(64,83)(65,84)(66,85)(67,72)(69,79)(74,82)(75,100)(77,96)(78,103)(80,95)(81,98)(87,102)(88,110)(89,93)(90,107)(91,108)(92,109)(94,99)(97,105)(101,106)(104,115)(111,116)(112,114)(113,117);(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)(54,55,58,64,59,66,78,91,60,63,77,87,80,88,104,111,61,65,79,90,81,92,105,113,57,72,74,89,75,99,101,112)(56,67,69,93,70,94,97,114,68,62,82,83,95,85,106,108,71,86,76,102,98,110,103,116,73,84,96,107,100,109,115,117)Polycyclic presentation:
2^8,53|a^2=d,c^2=h,d^2=f,f^2=g,g^2=h,b^a=bc,c^a=ce,e^a=eh,c^b=ch,d^b=deh,i^b=i^52,d^c=dh1196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56912);