Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C79×#1407 ⋊ C2 |
| Sylow | C79 ⋊ #13678 |
400 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 3 generators on 111 points:
(1,2)(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)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)(77,78)(80,82,85,92)(81,87,89,105)(83,95,93,110)(84,98,97,91)(86,100,94,111)(88,103,107,104)(90,99,108,96)(101,102,106,109);(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)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,87)(83,94)(84,88)(85,89)(86,93)(90,109)(91,104)(92,105)(95,111)(96,106)(97,107)(98,103)(99,101)(100,110)(102,108);(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)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(81,86)(83,93)(84,97)(87,102)(88,101)(89,94)(90,108)(95,110)(100,103)(104,111)(105,109)(106,107)Polycyclic presentation:
2^8,79|c^2=h,d^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,f^a=fg,i^a=i^78,d^b=dh,e^b=efgh,g^b=gh,i^b=i^78,d^c=df,f^c=fh,g^c=gh,i^c=i^78,e^d=egh,f^d=fh,f^e=fh568 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90310);