Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C79×#1401 ⋊ C2 |
| Sylow | C79 ⋊ #13671 |
284 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 59 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)(80,82)(81,88)(83,94)(84,97)(85,96)(86,98)(87,111)(89,116)(90,118)(91,117)(92,119)(93,105)(95,106)(99,114)(100,103)(101,108)(102,128)(104,110)(107,140)(109,130)(112,133)(113,123)(115,131)(120,136)(121,139)(122,141)(124,129)(125,132)(126,142)(127,138)(134,143)(135,137);(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)(81,87)(83,100)(84,95)(85,108)(86,98)(88,111)(89,121)(90,112)(91,125)(92,115)(93,99)(94,103)(96,101)(97,106)(102,134)(104,136)(105,114)(107,113)(109,129)(110,120)(116,139)(117,132)(118,133)(119,131)(122,142)(123,140)(124,130)(126,141)(127,137)(128,143)(135,138);(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)(80,81,86,92)(82,93,98,118)(83,99,104,133)(84,105,106,90)(85,107,109,139)(87,110,115,94)(88,97,119,95)(89,120,123,103)(91,124,126,101)(96,117,130,142)(100,125,136,141)(102,111,138,131)(108,121,129,140)(112,127,114,128)(113,134,116,135)(122,137,132,143)Polycyclic presentation:
2^8,79|a^2=h,d^2=fg,e^2=h,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,f^a=fg,g^a=gh,i^a=i^78,d^b=df,f^b=fg,g^b=gh,i^b=i^78,e^c=eh2221 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90268);