Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #12047 |
212 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 91 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)(80,83,84,97,86,99,102,111,87,100,92,103,85,98,101,110)(81,88,90,105,91,106,94,107,82,93,95,108,96,109,89,104);(80,82)(81,87)(83,93)(84,95)(85,91)(86,96)(88,100)(89,102)(90,92)(94,101)(97,108)(98,106)(99,109)(103,105)(104,111)(107,110);(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)(80,81,84,90,86,91,102,94,87,82,92,95,85,96,101,89)(83,93,97,108,99,109,111,104,100,88,103,105,98,106,110,107)Polycyclic presentation:
2^8,79|a^2=e,c^2=e,d^2=fh,e^2=g,f^2=h,g^2=h,b^a=bd,c^a=ch,d^a=df,f^a=fh,i^a=i^78,d^b=df,f^b=fh,i^c=i^781780 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 81329);