Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C53×C22⋊C32 ⋊ C2 |
| Sylow | C53 ⋊ #7335 |
158 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 125 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 2 generators on 125 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)(55,58)(57,61)(59,60)(62,64)(63,70)(65,81)(66,84)(67,79)(68,77)(69,80)(71,94)(72,97)(73,92)(74,76)(75,93)(78,87)(82,105)(83,109)(85,112)(86,90)(88,106)(89,108)(91,100)(95,103)(96,118)(98,120)(99,111)(101,104)(102,117)(107,114)(110,124)(113,115)(116,122)(119,123)(121,125);(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)(56,60,61,58)(57,59)(62,63,66,72,67,73,85,98,68,74,86,99,88,101,113,121,69,75,87,100,89,102,114,122,65,71,82,95,83,96,110,119)(64,76,78,103,79,104,107,123,77,93,105,97,106,117,124,120,80,94,84,111,108,118,112,125,81,70,90,91,109,92,115,116)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,c^b=ch,d^b=deh,i^b=i^522156 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56908);