Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C53×#2253 ⋊ C2 |
| Sylow | C53 ⋊ #12463 |
172 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 59 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)(59,82)(60,76)(61,78)(62,86)(64,91)(65,96)(66,92)(67,94)(68,97)(70,102)(71,107)(72,103)(73,105)(74,95)(77,80)(79,110)(81,90)(83,111)(84,93)(85,112)(87,115)(88,101)(89,114)(98,113)(99,116)(100,109)(104,106)(108,117);(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)(54,56,59,71,60,72,81,85,61,73,83,108,80,106,58,70)(55,62,79,99,66,88,95,100,67,89,65,87,84,98,64,68)(57,69,82,107,76,103,90,112,78,105,111,117,77,104,75,102)(63,86,110,116,92,101,74,109,94,114,96,115,93,113,91,97);(54,55,61,67)(56,68,73,100)(57,74)(58,79,81,65)(59,64,83,95)(60,84,80,66)(62,85,89,70)(63,90)(69,101)(71,98,108,88)(72,87,106,99)(75,94)(76,110)(77,96)(78,91)(82,92)(86,103)(93,111)(97,112)(102,109)(104,114)(105,113)(107,116)(115,117)Polycyclic presentation:
2^8,53|a^2=fg,b^2=df,d^2=fh,e^2=g,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fh,g^a=gh,e^c=egh,g^c=gh,i^c=i^521025 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 83958);