Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #7388 |
118 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 118 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)(55,62)(57,76)(58,71)(59,84)(60,72)(61,74)(63,91)(64,96)(65,89)(66,98)(67,90)(68,99)(69,104)(70,77)(73,85)(75,103)(78,107)(79,108)(80,113)(81,86)(82,105)(83,88)(87,97)(92,117)(93,100)(94,109)(95,101)(102,112)(106,115)(110,111)(114,116);(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)(54,55,58,64,60,65,82,92,61,67,77,97,85,66,59,83)(56,68,70,100,72,102,84,101,74,103,71,109,73,110,105,91)(57,75,78,93,80,111,104,95,81,99,115,94,116,112,79,63)(62,86,87,107,89,114,88,69,90,76,96,106,98,113,117,108)Polycyclic presentation:
2^8,53|a^2=d,c^2=egh,d^2=f,e^2=gh,f^2=h,g^2=h,b^a=bc,c^a=ce,e^a=eg,g^a=gh,i^a=i^52,c^b=ceh,d^b=dh,e^b=eg,g^b=gh1196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57033);