Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #13620 |
290 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 111 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:
(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)(56,68)(61,84)(67,96)(69,98)(70,72)(71,99)(74,107)(81,101)(83,100)(85,95)(86,113)(88,115)(93,117)(97,103)(102,116)(108,109);(54,56)(55,61)(57,74)(58,70)(59,81)(60,68)(62,88)(63,85)(64,93)(65,95)(66,84)(67,73)(69,77)(71,75)(72,79)(76,108)(78,107)(80,86)(82,101)(83,87)(89,102)(90,116)(91,115)(92,113)(94,117)(96,106)(97,104)(98,112)(99,110)(100,114)(103,105)(109,111);(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)(54,55,58,63,60,66,79,65)(56,67,70,97,68,96,72,103)(57,73,76,104,78,106,111,105)(59,80,75,64,82,92,110,94)(61,83,85,98,84,100,95,69)(62,87,89,112,91,114,90,77)(71,102,101,115,99,116,81,88)(74,93,108,113,107,117,109,86)Polycyclic presentation:
2^8,53|a^2=e,d^2=fg,e^2=h,f^2=gh,g^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,i^a=i^52,c^b=ch,d^b=df,f^b=fg,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, 90023);