Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #13668 |
284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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)(83,99)(88,115)(92,121)(93,109)(97,127)(98,130)(101,113)(102,133)(114,141)(116,128)(122,126)(123,131)(125,142)(129,135)(132,136)(134,140);(80,82)(81,87)(83,98)(84,104)(85,108)(86,94)(88,114)(89,118)(90,120)(91,110)(92,97)(93,101)(95,100)(96,105)(99,130)(102,136)(103,111)(106,138)(107,112)(109,113)(115,141)(116,142)(117,124)(119,143)(121,127)(122,135)(123,140)(125,128)(126,129)(131,134)(132,133)(137,139);(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)(80,81,86,91)(82,92,94,121)(83,97,99,127)(84,103,106,137)(85,107,105,90)(87,109,110,93)(88,113,115,101)(89,117,119,100)(95,125,124,142)(96,126,108,122)(98,118,130,143)(102,135,133,129)(104,114,138,141)(111,136,139,132)(112,123,120,131)(116,134,128,140)Polycyclic presentation:
2^8,79|a^2=h,d^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,f^a=fg,g^a=gh,i^a=i^78,d^b=df,e^b=eh,f^b=fg,g^b=gh,d^c=dh1279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90246);