Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C79 ⋊ #7382 |
118 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 118 conjugacy classes of subgroups — too many to draw. Only its 55 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 — 2 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)(80,82)(81,89)(83,101)(84,105)(85,111)(86,98)(87,97)(88,99)(90,115)(91,120)(92,116)(93,117)(94,123)(95,103)(96,109)(100,126)(102,132)(104,128)(106,129)(107,127)(108,136)(110,114)(112,133)(113,122)(118,141)(119,125)(121,138)(124,130)(131,134)(135,143)(137,140)(139,142);(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)(80,81,84,91,86,90,107,118,87,92,108,121,83,100,102,130,88,93,109,122,103,119,133,142,85,110,106,137,104,123,134,143)(82,94,96,124,98,89,112,113,97,115,129,139,101,116,131,140,99,126,105,135,95,117,127,120,111,125,136,141,128,114,132,138)Polycyclic presentation:
2^8,79|a^2=d,c^2=e,d^2=f,e^2=h,f^2=g,g^2=h,b^a=bc,c^a=ce,e^a=eh,i^a=i^78,c^b=ceh,d^b=dh,e^b=eh2248 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 57015);