Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #13556 |
290 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 143 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:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(82,93)(87,92)(94,97)(95,116)(96,117)(104,110)(105,114)(106,115)(118,121)(119,122)(120,137)(127,133)(128,134)(129,136)(138,139)(141,143);(80,82)(81,87)(83,97)(84,95)(85,96)(86,93)(88,92)(89,110)(90,105)(91,106)(94,100)(98,121)(99,122)(101,120)(102,116)(103,117)(104,107)(108,114)(109,115)(111,133)(112,134)(113,129)(118,124)(119,125)(123,139)(126,137)(127,130)(128,131)(132,136)(135,143)(138,140)(141,142);(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)(80,81,83,89,84,90,98,111,85,91,99,112,101,113,123,135,86,88,100,107,102,108,124,130,103,109,125,131,126,132,140,142)(82,92,94,110,95,114,118,133,96,115,119,134,120,136,138,143,93,87,97,104,116,105,121,127,117,106,122,128,137,129,139,141)Polycyclic presentation:
2^8,79|a^2=e,e^2=f,f^2=g,g^2=h,b^a=bd,d^a=dh,i^a=i^78,c^b=ch,e^b=eh3208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 89772);