Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C53×#368 ⋊ C2 |
| Sylow | C53 ⋊ #12840 |
354 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 119 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 — 3 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)(54,57)(55,63)(56,69)(58,75)(59,81)(60,76)(61,77)(62,84)(64,87)(65,74)(66,89)(67,91)(68,96)(70,98)(71,102)(72,99)(73,100)(78,108)(79,110)(80,107)(82,88)(83,111)(85,104)(86,113)(90,105)(92,112)(93,97)(94,115)(95,116)(101,117)(103,114)(106,109);(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)(54,56,68,95,60,72,80,101,61,73,79,83,59,71,58,70)(55,62,78,94,66,86,90,93,65,85,109,103,82,92,64,67)(57,69,96,116,76,99,107,117,77,100,110,111,81,102,75,98)(63,84,108,115,89,113,105,97,74,104,106,114,88,112,87,91);(54,55,59,66,61,65,60,82)(56,67,71,94,73,93,72,103)(57,74,76,89,77,63,81,88)(58,78,79,90,80,109,68,64)(62,83,86,101,85,95,92,70)(69,97,99,115,100,91,102,114)(75,106,96,105,107,108,110,87)(84,111,112,98,104,116,113,117)Polycyclic presentation:
2^8,53|a^2=f,b^2=dg,d^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,g^a=gh,f^c=fh,i^c=i^521196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85758);