Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #7365 |
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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)(55,61,62,77)(57,67)(58,68)(59,69)(60,66)(63,83,80,76)(64,78,81,99)(65,79,82,100)(70,87)(71,90)(72,91)(73,92)(74,88)(75,89)(84,105,102,97)(85,106,103,98)(86,101,104,114)(93,108)(94,109)(95,111)(96,110)(107,116,115,113)(112,117);(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)(54,55,57,63,58,64,71,84,59,65,72,85,73,86,95,107,60,62,70,80,74,81,93,102,75,82,94,103,96,104,112,115)(56,61,67,76,68,78,90,97,69,79,91,98,92,101,111,113,66,77,87,83,88,99,108,105,89,100,109,106,110,114,117,116)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,d^2=f,f^2=g,g^2=h,b^a=bc,c^a=ce,e^a=eh,i^a=i^52,c^b=ch,d^b=de,d^c=dh1508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56973);