Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #12916 |
370 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 131 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)(80,83)(81,89)(82,94)(84,103)(85,99)(86,98)(87,100)(88,108)(90,114)(91,113)(92,115)(93,119)(95,125)(96,123)(97,124)(101,112)(102,122)(104,130)(105,127)(106,128)(107,131)(109,133)(110,134)(111,121)(116,138)(117,139)(118,137)(120,141)(126,140)(129,132)(135,143)(136,142);(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)(80,82,85,97,86,95,105,107,87,96,106,126,84,102,104,129)(81,88,91,110,90,111,116,136,92,109,117,135,101,93,118,120)(83,94,99,124,98,125,127,131,100,123,128,140,103,122,130,132)(89,108,113,134,114,121,138,142,115,133,139,143,112,119,137,141);(80,81,85,91,86,90,105,116,87,92,106,117,84,101,104,118)(82,93,97,120,95,88,107,110,96,111,126,136,102,109,129,135)(83,89,99,113,98,114,127,138,100,115,128,139,103,112,130,137)(94,121,124,142,125,133,131,143,123,119,140,141,122,108,132,134)Polycyclic presentation:
2^8,79|a^2=f,b^2=f,d^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,d^b=dh,e^b=eh,i^b=i^78,d^c=dh2248 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 86047);