Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C79 ⋊ #7381 |
120 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 120 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)(81,88)(83,103)(84,97)(85,100)(86,99)(87,101)(89,117)(90,112)(91,125)(92,114)(93,113)(94,115)(95,102)(96,106)(98,104)(105,134)(107,128)(108,131)(109,130)(110,132)(111,116)(118,140)(119,127)(120,142)(121,138)(122,137)(123,139)(124,129)(126,133)(135,136)(141,143);(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)(80,81,84,90,86,92,109,121,85,93,108,122,83,102,105,133,87,94,110,123,106,89,116,118,104,91,124,120,107,119,135,141)(82,95,97,126,99,115,130,139,100,117,131,140,103,125,134,142,101,127,132,143,96,88,111,112,98,114,129,138,128,113,136,137)Polycyclic presentation:
2^8,79|a^2=d,c^2=eh,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=ce,e^b=eh2272 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 57012);