Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2141 ⋊ C2 |
| Sylow | C53 ⋊ #33588 |
680 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 163 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 121 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)(60,71)(65,86)(70,97)(72,100)(73,101)(85,112)(87,114)(88,105)(96,119)(98,111)(99,106)(102,118)(103,121)(104,115)(113,117)(116,120);(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)(58,61,64,77)(59,66,69,91)(60,70,71,97)(62,79,82,110)(63,84,80,76)(65,85,86,112)(67,93,94,109)(68,95,83,90)(72,103,100,121)(73,106,101,99)(74,107,108,78)(75,92,89,81)(87,116,114,120)(88,117,105,113)(96,118,119,102)(98,115,111,104);(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)(54,55,56,57)(58,60)(59,65)(61,70)(62,72)(63,73)(64,71)(66,85)(67,87)(68,88)(69,86)(74,96)(75,98)(76,99)(77,97)(78,102)(79,103)(80,101)(81,104)(82,100)(83,105)(84,106)(89,111)(90,113)(91,112)(92,115)(93,116)(94,114)(95,117)(107,118)(108,119)(109,120)(110,121);(55,57)(58,59,64,69)(60,65,71,86)(61,74,77,108)(62,78,82,107)(63,83,80,68)(66,89,91,75)(67,92,94,81)(70,96,97,119)(72,102,100,118)(73,105,101,88)(76,109,84,93)(79,95,110,90)(85,111,112,98)(87,115,114,104)(99,120,106,116)(103,117,121,113)Polycyclic presentation:
2^8,53|a^2=h,b^2=e,c^2=h,f^2=gh,g^2=h,b^a=be,c^a=cf,f^a=fg,g^a=gh,d^b=dh,i^b=i^52,f^c=fg,g^c=gh,i^c=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 323909);