Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #7113 |
254 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 87 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) = 20224 |
A minimal faithful permutation representation — 2 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)(88,90)(89,92)(91,95)(93,94)(96,97,100,103)(98,105,107,111)(99,108,106,102)(101,109,110,104);(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)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81,82,84,83,85,86,87)(88,89)(90,94,95,92)(91,93)(97,101)(98,104)(99,106)(102,111)(103,110)(105,108)(107,109)Polycyclic presentation:
2^8,79|a^2=d,b^2=h,c^2=fh,d^2=g,e^2=h,f^2=h,b^a=bc,c^a=ce,e^a=eh,f^a=fh,i^a=i^78,c^b=cf,d^b=defh,e^b=eh,f^b=fh,i^b=i^783178 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 56339);