Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #13648 |
184 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 143 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 143 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)(80,83,85,103,86,95,110,127,87,104,111,136,113,89,116,117,88,105,112,120,114,118,128,142,84,102,108,135,109,119,134,143)(81,90,92,100,93,122,125,133,91,121,123,107,124,138,141,139,94,101,126,82,96,98,130,99,106,132,137,97,129,115,140,131);(80,82)(81,89)(83,96)(84,107)(85,98)(86,99)(87,97)(88,100)(90,116)(91,118)(92,117)(93,105)(94,119)(95,106)(101,134)(102,124)(103,130)(104,129)(108,138)(109,139)(110,132)(111,115)(112,122)(113,131)(114,133)(120,125)(121,128)(123,142)(126,143)(127,137)(135,141)(136,140);(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)(80,81,85,92,86,93,110,125,87,91,111,123,113,124,116,141,88,94,112,126,114,96,128,130,84,106,108,137,109,129,134,140)(82,95,98,127,99,104,132,136,97,89,115,117,131,105,90,120,100,118,122,142,133,102,121,135,107,119,138,143,139,83,101,103)Polycyclic presentation:
2^8,79|a^2=e,c^2=e,d^2=h,e^2=f,f^2=g,g^2=h,b^a=bd,c^a=ch,d^a=dh,i^a=i^78,d^b=dh,i^c=i^782272 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90137);